On 8/11/2023 6:41 PM, Eram semper recta wrote:
> On Friday, 11 August 2023 at 21:00:46 UTC-4, Fritz Feldhase wrote:
>> On Saturday, August 12, 2023 at 1:57:49 AM UTC+2, Eram semper recta wrote:
>>> On Friday, 11 August 2023 at 19:07:30 UTC-4, Fritz Feldhase wrote:
>>>> On Saturday, August 12, 2023 at 12:34:56 AM UTC+2, Eram semper recta wrote:
>>>>> On Friday, 11 August 2023 at 17:32:04 UTC-4, Fritz Feldhase wrote:
>>>>>> On Friday, August 11, 2023 at 10:29:40 PM UTC+2, Eram semper recta wrote:
>>>>>>>
>>>>>>> Oh, wait a minute! You thought that y = (c - ax)/b does not include vertical lines?!
>>>>>>>
>>>>>> Exactly.
>>>>> [deleted psychotic nonsense]
>>>>> x=bc/a is a vertical line.
>>>> Please show us how you get this equation from the equation y = (c - ax)/b, you psyhotic idiot.
>>> I showed you, idiot.
>>>
>>> x=bc/a (Set y=0)
>>> y=c/b (Set x=0)
>>>
>>> Man, you're an idiot deluxe. This stuff is elementary.
>>> <drivel>
>> On Saturday, August 12, 2023 at 2:00:49 AM UTC+2, Eram semper recta wrote:
>>> On Friday, 11 August 2023 at 19:57:49 UTC-4, Eram semper recta wrote:
>>>> On Friday, 11 August 2023 at 19:07:30 UTC-4, Fritz Feldhase wrote:
>>>>> On Saturday, August 12, 2023 at 12:34:56 AM UTC+2, Eram semper recta wrote:
>>>>>> On Friday, 11 August 2023 at 17:32:04 UTC-4, Fritz Feldhase wrote:
>>>>>>> On Friday, August 11, 2023 at 10:29:40 PM UTC+2, Eram semper recta wrote:
>>>>>>>>
>>>>>>>> Oh, wait a minute! You thought that y = (c - ax)/b does not include vertical lines?!
>>>>>>>>
>>>>>>> Exactly.
>>>>>>>
>>>>>> x=bc/a is a vertical line.
>>>>>>
>>>>> Please show us how you get this equation from the equation y = (c - ax)/b, you psyhotic idiot.
>>>>>
>>>> I showed you, idiot.
>> No, you didn't.
>
> Sure I did. You're just being pigheaded because I showed you to be an idiot.
>
>>
>>>> x=bc/a (Set y=0)
>>
>> Please get professional help, soon!
>>
>> Hint: If y = 0 and x = bc/a, (x,y) is just a point not a "line", you psychotic asshole full of shit.
>
> How is x=bc/a a point, fucking stupid dipstick?!
>
> x=bc/a is the equation of a vertical line. Everyone is laughing at your stupidity and obstinance.
>
> Grow a brain, moron!
>
>>
>> Moreover, if x =/= 0, then neither a nor b nor c = 0. In this case the equation
>> y = (c - ax)/b
>> certainly does not specify a vertical line, you psychotic asshole.
>
> I said y = (c - ax)/b specifies a HORIZONTAL, you dipshit!! Take your Kraut straw man arguments elsewhere. Shove them up your arse!
>
>> Seems that I am a complete moron.
>
> YOU ARE INDEED an idiot DELUXE!

Usually, the x plane is horizontal and the y plane is vertical. Negative
x to the left, positive x to the right, positive y up and negative y
down. 2-ary. (x, y).

On Saturday, August 12, 2023 at 3:41:12 AM UTC+2, Eram semper recta wrote:
> On Friday, 11 August 2023 at 21:00:46 UTC-4, Fritz Feldhase wrote:

> > Hint: If y = 0 and x = bc/a, (x,y) is just a point not a "line", you psychotic asshole full of shit.
> >
> How is x=bc/a a point, fucking stupid dipstick?!

I WROTE

________ If y = 0 and x = bc/a, (x, y) is just a point not a "line" _______

YOU PSYCHOTIC ASSHOLE.

WHAT ARE YOU EVEN TALKING ABOUT?! SEEMS THAT YOU REALLY NEED PSYCHIATRIC TREATMENT!

Hint: No one claimed that "x=bc/a is a point". <facepalm>

> x=bc/a is the equation of a vertical line.

That wasen't your original claim YOU LYING PIECE OF SHIT!

I quoted: "Every line L (including vertical lines) is the set of all points whose coordinates (x, y) satisfy a linear equation; that is, L = {(x,y) : ax + by = c}, where a, b and c are fixed real numbers (called coefficients) such that a and b are not both zero."

To which you REPLIED: "Those points are not part of a line whose equation by the way, is y = (c - ax)/b. Chuckle."

Seems that you are just a mentally ill clown.

Hint:

> > If x =/= 0, then x=bc/a implies that neither a nor b nor c = 0.
> >
> > In this case the equation
> > y = (c - ax)/b
> > certainly does not specify a vertical line, you psychotic asshole.

> I said y = (c - ax)/b specifies a HORIZONTAL, you dipshit!

NO, YOU LYING PIECE OF SHIT!

Hint:

I quoted: "Every line L (including vertical lines) is the set of all points whose coordinates (x, y) satisfy a linear equation; that is, L = {(x,y) : ax + by = c}, where a, b and c are fixed real numbers (called coefficients) such that a and b are not both zero."

To which you REPLIED: "Those points are not part of a line whose equation by the way, is y = (c - ax)/b. Chuckle."

GOT THAT Du psychotisches Arschloch?

__________________________________________________________________

y = (c - ax)/b may specify ANY line _which is not a vertical line_.

On the other hand ax + by = c may specify EACH AND EVERY line.

That's why your reply"Those points are not part of a line whose equation by the way, is y = (c - ax)/b. Chuckle."

to

"Every line L (including vertical lines) is the set of all points whose coordinates (x, y) satisfy a linear equation; that is, L = {(x,y) : ax + by = c}, where a, b and c are fixed real numbers (called coefficients) such that a and b are not both zero."

is so idiotic!

Hint: NO, the equation of a line "in general" is NOT y = (c - ax)/b but ax + by = c (where a, b and c are fixed real numbers (called coefficients) such that a and b are not both zero).

Since you - Mr. Rectum - seem to be mentally impaired, I will retreat from this discussion.

I wish you good luck.

On Friday, 11 August 2023 at 22:38:32 UTC-4, Chris M. Thomasson wrote:
> On 8/11/2023 6:41 PM, Eram semper recta wrote:
> > On Friday, 11 August 2023 at 21:00:46 UTC-4, Fritz Feldhase wrote:
> >> On Saturday, August 12, 2023 at 1:57:49 AM UTC+2, Eram semper recta wrote:
> >>> On Friday, 11 August 2023 at 19:07:30 UTC-4, Fritz Feldhase wrote:
> >>>> On Saturday, August 12, 2023 at 12:34:56 AM UTC+2, Eram semper recta wrote:
> >>>>> On Friday, 11 August 2023 at 17:32:04 UTC-4, Fritz Feldhase wrote:
> >>>>>> On Friday, August 11, 2023 at 10:29:40 PM UTC+2, Eram semper recta wrote:
> >>>>>>>
> >>>>>>> Oh, wait a minute! You thought that y = (c - ax)/b does not include vertical lines?!
> >>>>>>>
> >>>>>> Exactly.
> >>>>> [deleted psychotic nonsense]
> >>>>> x=bc/a is a vertical line.
> >>>> Please show us how you get this equation from the equation y = (c - ax)/b, you psyhotic idiot.
> >>> I showed you, idiot.
> >>>
> >>> x=bc/a (Set y=0)
> >>> y=c/b (Set x=0)
> >>>
> >>> Man, you're an idiot deluxe. This stuff is elementary.
> >>> <drivel>
> >> On Saturday, August 12, 2023 at 2:00:49 AM UTC+2, Eram semper recta wrote:
> >>> On Friday, 11 August 2023 at 19:57:49 UTC-4, Eram semper recta wrote:
> >>>> On Friday, 11 August 2023 at 19:07:30 UTC-4, Fritz Feldhase wrote:
> >>>>> On Saturday, August 12, 2023 at 12:34:56 AM UTC+2, Eram semper recta wrote:
> >>>>>> On Friday, 11 August 2023 at 17:32:04 UTC-4, Fritz Feldhase wrote:
> >>>>>>> On Friday, August 11, 2023 at 10:29:40 PM UTC+2, Eram semper recta wrote:
> >>>>>>>>
> >>>>>>>> Oh, wait a minute! You thought that y = (c - ax)/b does not include vertical lines?!
> >>>>>>>>
> >>>>>>> Exactly.
> >>>>>>>
> >>>>>> x=bc/a is a vertical line.
> >>>>>>
> >>>>> Please show us how you get this equation from the equation y = (c - ax)/b, you psyhotic idiot.
> >>>>>
> >>>> I showed you, idiot.
> >> No, you didn't.
> >
> > Sure I did. You're just being pigheaded because I showed you to be an idiot.
> >
> >>
> >>>> x=bc/a (Set y=0)
> >>
> >> Please get professional help, soon!
> >>
> >> Hint: If y = 0 and x = bc/a, (x,y) is just a point not a "line", you psychotic asshole full of shit.
> >
> > How is x=bc/a a point, fucking stupid dipstick?!
> >
> > x=bc/a is the equation of a vertical line. Everyone is laughing at your stupidity and obstinance.
> >
> > Grow a brain, moron!
> >
> >>
> >> Moreover, if x =/= 0, then neither a nor b nor c = 0. In this case the equation
> >> y = (c - ax)/b
> >> certainly does not specify a vertical line, you psychotic asshole.
> >
> > I said y = (c - ax)/b specifies a HORIZONTAL, you dipshit!! Take your Kraut straw man arguments elsewhere. Shove them up your arse!
> >
> >> Seems that I am a complete moron.
> >
> > YOU ARE INDEED an idiot DELUXE!
> Usually, the x plane is horizontal and the y plane is vertical. Negative
> x to the left, positive x to the right, positive y up and negative y
> down. 2-ary. (x, y).

Relevance? None.

Anyone who claims that y=c/b is not a horizontal line and that x = bc/a is not a vertical line seriously needs to go back to middle school.

On Friday, 11 August 2023 at 23:29:20 UTC-4, Fritz Feldhase wrote:
> Since you - Mr. Rectum - seem to be mentally impaired, I will retreat from this discussion.
>
> I wish you good luck.

Man, you're an idiot. That's all there is to it.

You wrote a ton of crap and I kept correcting you over and over again. You act like a defiant 5 year old - just like your cousin Donald Trump.

<PLONK>

On Friday, 11 August 2023 at 23:22:44 UTC-4, Fritz Feldhase wrote:

> Hint: NO, the equation of a line "in general" is NOT y = (c - ax)/b but ax + by = c (where a, b and c are fixed real numbers (called coefficients) such that a and b are not both zero).

<drivel ignored>

y = (c - ax)/b and ax + by = c are the SAME equation, you fucking idiot!!!!

And yes, a line DOES NOT consist of points. A line is a distance between two points.

The equation serves as a "roadmap" of how to traverse a given line - NOTHING MORE, NOTHING LESS.

Grow a brain, you STUPID schmuck.

What are you smoking all day? Must be a hell of a drug.
I have never heard more crazy gibberish.

Hint: The line is infinite at both ends, nothing to do
with DISTANCE between two points. You are confusing

infinite line with line segment. This here is an infinite line,
not a line segment:

a*x + b*y + c = 0

If you want a line segment you might use two points (x1,y1)
and (x2,y2) on the line, and then state it as:

a*x + b*y + c = 0 &
min(x1,x2) < x & x < max(x1,x2) &
min(y1,y2) < y & y < max(y1,y2) &

You can the parameterize based on a parameter t into two
functions x : [0,1] -> R and y : [0,1] -> R, so that:

a*x(t) + b*y(t) + c = 0
min(x1,x2) < x(t) & x(t) < max(x1,x2) &
min(y1,y2) < y(t) & y(t) < max(y1,y2) &

The parameterization is:

x(t) = x1+(x2-x1)*t
y(t) = y1+(y2-y1)*t

Works always, also for horizontal and vertical lines.
For an infinite line just change the parameter domain
from interval [0,1] to the full real line R.

Eram semper recta schrieb am Samstag, 12. August 2023 um 03:44:20 UTC+2:
> On Friday, 11 August 2023 at 20:11:58 UTC-4, Mild Shock wrote:
> > Not understanding how:
> > a*x + b*y + c = 0
> > works, and then starting to talk about road signs,
> Oh poor idiot Jan Burse. You've hit a brick wall on that one? LMAO
>
> a*x + b*y + c = 0 is the equation of a straight line.
>
> Now, points are to that line as a roadmap. They are not
> part of a line which is defined as the DISTANCE between two points.

Corr.: The two points would be distinct, and I guess
we want to include them, so the equation and
inequation would be:

a*x + b*y + c = 0 &
min(x1,x2) =< x & x =< max(x1,x2) &
min(y1,y2) =< y & y =< max(y1,y2) &

Using less than or equal =<, instead of only less than <.

Mild Shock schrieb am Samstag, 12. August 2023 um 14:52:33 UTC+2:
> What are you smoking all day? Must be a hell of a drug.
> I have never heard more crazy gibberish.
>
> Hint: The line is infinite at both ends, nothing to do
> with DISTANCE between two points. You are confusing
>
> infinite line with line segment. This here is an infinite line,
> not a line segment:
> a*x + b*y + c = 0
> If you want a line segment you might use two points (x1,y1)
> and (x2,y2) on the line, and then state it as:
>
> a*x + b*y + c = 0 &
> min(x1,x2) < x & x < max(x1,x2) &
> min(y1,y2) < y & y < max(y1,y2) &
>
> You can the parameterize based on a parameter t into two
> functions x : [0,1] -> R and y : [0,1] -> R, so that:
>
> a*x(t) + b*y(t) + c = 0
> min(x1,x2) < x(t) & x(t) < max(x1,x2) &
> min(y1,y2) < y(t) & y(t) < max(y1,y2) &
>
> The parameterization is:
>
> x(t) = x1+(x2-x1)*t
> y(t) = y1+(y2-y1)*t
>
> Works always, also for horizontal and vertical lines.
> For an infinite line just change the parameter domain
> from interval [0,1] to the full real line R.
> Eram semper recta schrieb am Samstag, 12. August 2023 um 03:44:20 UTC+2:
> > On Friday, 11 August 2023 at 20:11:58 UTC-4, Mild Shock wrote:
> > > Not understanding how:
> > > a*x + b*y + c = 0
> > > works, and then starting to talk about road signs,
> > Oh poor idiot Jan Burse. You've hit a brick wall on that one? LMAO
> >
> > a*x + b*y + c = 0 is the equation of a straight line.
> >
> > Now, points are to that line as a roadmap. They are not
> > part of a line which is defined as the DISTANCE between two points.

On Saturday, August 12, 2023 at 2:52:33 PM UTC+2, Mild Shock wrote:

> This here is an infinite line, not a line segment: a*x + b*y + c = 0

Actually, (strictly speaking) it's not a line, but an equation (specifying a line).

The corresponding line may be defined as the set {(x, y) e IR x IR : a*x + b*y + c = 0}.

"Every line L (including vertical lines) is the set of all points whose coordinates (x, y) satisfy a linear equation; that is,

L = {(x, y) : ax + by = c},

where a, b and c are fixed real numbers (called coefficients) such that a and b are not both zero." (Wikipedia)

On Saturday, August 12, 2023 at 2:43:36 PM UTC+2, Eram semper recta wrote:

> y = (c - ax)/b and ax + by = c are the SAME equation

It's clear that you are suffering from a psyhosis (or some sort of mental breakdown), man.

Nuff said.

On 8/12/2023 5:39 AM, Eram semper recta wrote:
> On Friday, 11 August 2023 at 22:38:32 UTC-4, Chris M. Thomasson wrote:
>> On 8/11/2023 6:41 PM, Eram semper recta wrote:
>>> On Friday, 11 August 2023 at 21:00:46 UTC-4, Fritz Feldhase wrote:
>>>> On Saturday, August 12, 2023 at 1:57:49 AM UTC+2, Eram semper recta wrote:
>>>>> On Friday, 11 August 2023 at 19:07:30 UTC-4, Fritz Feldhase wrote:
>>>>>> On Saturday, August 12, 2023 at 12:34:56 AM UTC+2, Eram semper recta wrote:
>>>>>>> On Friday, 11 August 2023 at 17:32:04 UTC-4, Fritz Feldhase wrote:
>>>>>>>> On Friday, August 11, 2023 at 10:29:40 PM UTC+2, Eram semper recta wrote:
>>>>>>>>>
>>>>>>>>> Oh, wait a minute! You thought that y = (c - ax)/b does not include vertical lines?!
>>>>>>>>>
>>>>>>>> Exactly.
>>>>>>> [deleted psychotic nonsense]
>>>>>>> x=bc/a is a vertical line.
>>>>>> Please show us how you get this equation from the equation y = (c - ax)/b, you psyhotic idiot.
>>>>> I showed you, idiot.
>>>>>
>>>>> x=bc/a (Set y=0)
>>>>> y=c/b (Set x=0)
>>>>>
>>>>> Man, you're an idiot deluxe. This stuff is elementary.
>>>>> <drivel>
>>>> On Saturday, August 12, 2023 at 2:00:49 AM UTC+2, Eram semper recta wrote:
>>>>> On Friday, 11 August 2023 at 19:57:49 UTC-4, Eram semper recta wrote:
>>>>>> On Friday, 11 August 2023 at 19:07:30 UTC-4, Fritz Feldhase wrote:
>>>>>>> On Saturday, August 12, 2023 at 12:34:56 AM UTC+2, Eram semper recta wrote:
>>>>>>>> On Friday, 11 August 2023 at 17:32:04 UTC-4, Fritz Feldhase wrote:
>>>>>>>>> On Friday, August 11, 2023 at 10:29:40 PM UTC+2, Eram semper recta wrote:
>>>>>>>>>>
>>>>>>>>>> Oh, wait a minute! You thought that y = (c - ax)/b does not include vertical lines?!
>>>>>>>>>>
>>>>>>>>> Exactly.
>>>>>>>>>
>>>>>>>> x=bc/a is a vertical line.
>>>>>>>>
>>>>>>> Please show us how you get this equation from the equation y = (c - ax)/b, you psyhotic idiot.
>>>>>>>
>>>>>> I showed you, idiot.
>>>> No, you didn't.
>>>
>>> Sure I did. You're just being pigheaded because I showed you to be an idiot.
>>>
>>>>
>>>>>> x=bc/a (Set y=0)
>>>>
>>>> Please get professional help, soon!
>>>>
>>>> Hint: If y = 0 and x = bc/a, (x,y) is just a point not a "line", you psychotic asshole full of shit.
>>>
>>> How is x=bc/a a point, fucking stupid dipstick?!
>>>
>>> x=bc/a is the equation of a vertical line. Everyone is laughing at your stupidity and obstinance.
>>>
>>> Grow a brain, moron!
>>>
>>>>
>>>> Moreover, if x =/= 0, then neither a nor b nor c = 0. In this case the equation
>>>> y = (c - ax)/b
>>>> certainly does not specify a vertical line, you psychotic asshole.
>>>
>>> I said y = (c - ax)/b specifies a HORIZONTAL, you dipshit!! Take your Kraut straw man arguments elsewhere. Shove them up your arse!
>>>
>>>> Seems that I am a complete moron.
>>>
>>> YOU ARE INDEED an idiot DELUXE!
>> Usually, the x plane is horizontal and the y plane is vertical. Negative
>> x to the left, positive x to the right, positive y up and negative y
>> down. 2-ary. (x, y).
>
> Relevance? None.
>
> Anyone who claims that y=c/b is not a horizontal line and that x = bc/a is not a vertical line seriously needs to go back to middle school.

horizontal is usually the x axis, vertical is usually the y axis.

On 8/12/2023 11:01 AM, Chris M. Thomasson wrote:
> On 8/12/2023 5:39 AM, Eram semper recta wrote:
>> On Friday, 11 August 2023 at 22:38:32 UTC-4, Chris M. Thomasson wrote:
>>> On 8/11/2023 6:41 PM, Eram semper recta wrote:
>>>> On Friday, 11 August 2023 at 21:00:46 UTC-4, Fritz Feldhase wrote:
>>>>> On Saturday, August 12, 2023 at 1:57:49 AM UTC+2, Eram semper recta
>>>>> wrote:
>>>>>> On Friday, 11 August 2023 at 19:07:30 UTC-4, Fritz Feldhase wrote:
>>>>>>> On Saturday, August 12, 2023 at 12:34:56 AM UTC+2, Eram semper
>>>>>>> recta wrote:
>>>>>>>> On Friday, 11 August 2023 at 17:32:04 UTC-4, Fritz Feldhase wrote:
>>>>>>>>> On Friday, August 11, 2023 at 10:29:40 PM UTC+2, Eram semper
>>>>>>>>> recta wrote:
>>>>>>>>>>
>>>>>>>>>> Oh, wait a minute! You thought that y = (c - ax)/b does not
>>>>>>>>>> include vertical lines?!
>>>>>>>>>>
>>>>>>>>> Exactly.
>>>>>>>> [deleted psychotic nonsense]
>>>>>>>> x=bc/a is a vertical line.
>>>>>>> Please show us how you get this equation from the equation y = (c
>>>>>>> - ax)/b, you psyhotic idiot.
>>>>>> I showed you, idiot.
>>>>>>
>>>>>> x=bc/a (Set y=0)
>>>>>> y=c/b (Set x=0)
>>>>>>
>>>>>> Man, you're an idiot deluxe. This stuff is elementary.
>>>>>> <drivel>
>>>>> On Saturday, August 12, 2023 at 2:00:49 AM UTC+2, Eram semper recta
>>>>> wrote:
>>>>>> On Friday, 11 August 2023 at 19:57:49 UTC-4, Eram semper recta wrote:
>>>>>>> On Friday, 11 August 2023 at 19:07:30 UTC-4, Fritz Feldhase wrote:
>>>>>>>> On Saturday, August 12, 2023 at 12:34:56 AM UTC+2, Eram semper
>>>>>>>> recta wrote:
>>>>>>>>> On Friday, 11 August 2023 at 17:32:04 UTC-4, Fritz Feldhase wrote:
>>>>>>>>>> On Friday, August 11, 2023 at 10:29:40 PM UTC+2, Eram semper
>>>>>>>>>> recta wrote:
>>>>>>>>>>>
>>>>>>>>>>> Oh, wait a minute! You thought that y = (c - ax)/b does not
>>>>>>>>>>> include vertical lines?!
>>>>>>>>>>>
>>>>>>>>>> Exactly.
>>>>>>>>>>
>>>>>>>>> x=bc/a is a vertical line.
>>>>>>>>>
>>>>>>>> Please show us how you get this equation from the equation y =
>>>>>>>> (c - ax)/b, you psyhotic idiot.
>>>>>>>>
>>>>>>> I showed you, idiot.
>>>>> No, you didn't.
>>>>
>>>> Sure I did. You're just being pigheaded because I showed you to be
>>>> an idiot.
>>>>
>>>>>
>>>>>>> x=bc/a (Set y=0)
>>>>>
>>>>> Please get professional help, soon!
>>>>>
>>>>> Hint: If y = 0 and x = bc/a, (x,y) is just a point not a "line",
>>>>> you psychotic asshole full of shit.
>>>>
>>>> How is x=bc/a a point, fucking stupid dipstick?!
>>>>
>>>> x=bc/a is the equation of a vertical line. Everyone is laughing at
>>>> your stupidity and obstinance.
>>>>
>>>> Grow a brain, moron!
>>>>
>>>>>
>>>>> Moreover, if x =/= 0, then neither a nor b nor c = 0. In this case
>>>>> the equation
>>>>> y = (c - ax)/b
>>>>> certainly does not specify a vertical line, you psychotic asshole.
>>>>
>>>> I said y = (c - ax)/b specifies a HORIZONTAL, you dipshit!! Take
>>>> your Kraut straw man arguments elsewhere. Shove them up your arse!
>>>>
>>>>> Seems that I am a complete moron.
>>>>
>>>> YOU ARE INDEED an idiot DELUXE!
>>> Usually, the x plane is horizontal and the y plane is vertical. Negative
>>> x to the left, positive x to the right, positive y up and negative y
>>> down. 2-ary. (x, y).
>>
>> Relevance? None.
>>
>> Anyone who claims that y=c/b is not a horizontal line and that x =
>> bc/a is not a vertical line seriously needs to go back to middle school.
>
> horizontal is usually the x axis, vertical is usually the y axis.

y is usually rise and x is usually run in the 2-ary plane (x, y)

On 8/12/2023 5:52 AM, Mild Shock wrote:
>
> What are you smoking all day? Must be a hell of a drug.
> I have never heard more crazy gibberish.
>
> Hint: The line is infinite at both ends, nothing to do
> with DISTANCE between two points. You are confusing
[...]

Right. Give me a point and a normalized direction and I can construct a
line that extends for infinity from that point in the direction.

Give me a normalized direction only and I can create an infinite line
from any origin point, in n-ary.

On 8/12/2023 11:04 AM, Chris M. Thomasson wrote:
> On 8/12/2023 5:52 AM, Mild Shock wrote:
>>
>> What are you smoking all day? Must be a hell of a drug.
>> I have never heard more crazy gibberish.
>>
>> Hint: The line is infinite at both ends, nothing to do
>> with DISTANCE between two points. You are confusing
> [...]
>
> Right. Give me a point and a normalized direction and I can construct a
> line that extends for infinity from that point in the direction.
>
> Give me a normalized direction only and I can create an infinite line
> from any origin point, in n-ary.
>
>

p0 = (0, 0)

dir = (cos(a), sin(a))

That is a point and a normalized direction. To get the opposite
normalized direction:

(cos(a + pi), sin(a + pi))

Pretty simple.

Chris M. Thomasson explained on 8/12/2023 :
> On 8/12/2023 5:52 AM, Mild Shock wrote:
>>
>> What are you smoking all day? Must be a hell of a drug.
>> I have never heard more crazy gibberish.
>>
>> Hint: The line is infinite at both ends, nothing to do
>> with DISTANCE between two points. You are confusing
> [...]
>
> Right. Give me a point and a normalized direction and I can construct a line
> that extends for infinity from that point in the direction.

And the other opposite direction, else it is a ray. Also, the said line
must be assumed to be straight.

Some say all "lines" are straight lines, other say straight line is a
special case of line (lines can be curved) like a square is a special
case of rectangle and circle a special case of ellipse.

Like "series" refers to sums of certain infinite sequences, yet some
say "infinite series" which is redundant and "straight line" is
redundant if your "lines" are defined as being straight as most folks
believe.

> Give me a normalized direction only and I can create an infinite line from
> any origin point, in n-ary.

Point slope form.

https://www.mathsisfun.com/algebra/line-equation-point-slope.html

On Saturday, 12 August 2023 at 10:34:54 UTC-4, Fritz Feldhase wrote:
> On Saturday, August 12, 2023 at 2:43:36 PM UTC+2, Eram semper recta wrote:
>
> > y = (c - ax)/b and ax + by = c are the SAME equation
> It's clear that you are suffering from a psyhosis (or some sort of mental breakdown), man.

You are definitely suffering from psychosis because no one will deny that y = (c - ax)/b and ax + by = c are the SAME equation.

> Nuff said.

Said the crank for the 16th time.

Fritzy Boy is the same type of crank as here, that would say, this
sentence is wrong. "DNA expresses enzymes".

And tends to correct you, to the correct thing is: "DNA expresses
RNA, and RNA expresses enzymes".

Who cares?

Fritz Feldhase schrieb am Samstag, 12. August 2023 um 16:34:41 UTC+2:
> On Saturday, August 12, 2023 at 2:52:33 PM UTC+2, Mild Shock wrote:
>
> > This here is an infinite line, not a line segment: a*x + b*y + c = 0
> Actually, (strictly speaking) it's not a line, but an equation (specifying a line).
>
> The corresponding line may be defined as the set {(x, y) e IR x IR : a*x + b*y + c = 0}.
> "Every line L (including vertical lines) is the set of all points whose coordinates (x, y) satisfy a linear equation; that is,
> L = {(x, y) : ax + by = c},
>
> where a, b and c are fixed real numbers (called coefficients) such that a and b are not both zero." (Wikipedia)

In as far Category Theory and subsequently Categorical Logic
has some therapeutic value. The DNA/RNA example is from here:

Category Theory for the Sciences
"Application 2.2.1.1. The central dogma of molecular
biology is that “DNA codes for RNA codes for protein”.
That is, there is a function from DNA triplets to RNA triplets
and a function from RNA triplets to amino acids. But
sometimes we just want to discuss the translation from
DNA to amino acids, and this is the composite of the other two"
https://math.mit.edu/~dspivak/CT4S.pdf

Category Theory see everything through the lense of
function composition. Quite consequently even.

Mild Shock schrieb am Sonntag, 13. August 2023 um 12:25:28 UTC+2:
> Fritzy Boy is the same type of crank as here, that would say, this
> sentence is wrong. "DNA expresses enzymes".
>
> And tends to correct you, to the correct thing is: "DNA expresses
> RNA, and RNA expresses enzymes".
>
> Who cares?
> Fritz Feldhase schrieb am Samstag, 12. August 2023 um 16:34:41 UTC+2:
> > On Saturday, August 12, 2023 at 2:52:33 PM UTC+2, Mild Shock wrote:
> >
> > > This here is an infinite line, not a line segment: a*x + b*y + c = 0
> > Actually, (strictly speaking) it's not a line, but an equation (specifying a line).
> >
> > The corresponding line may be defined as the set {(x, y) e IR x IR : a*x + b*y + c = 0}.
> > "Every line L (including vertical lines) is the set of all points whose coordinates (x, y) satisfy a linear equation; that is,
> > L = {(x, y) : ax + by = c},
> >
> > where a, b and c are fixed real numbers (called coefficients) such that a and b are not both zero." (Wikipedia)

The idea to require that we turn an equation:

a*x + b*y + c = 0

Into a set of pairs:

{(x, y) e IR x IR : a*x + b*y + c = 0}

Is also a sign of a certain brain wash. Who says
that every Category Cat must end in the Category Set?
Are there Categories Cat that are not mappable to

the Category Set? Historically, if we locate Algebraic
Geometry with Rene Descartes (1596 - 1650), there was
no Georg Cantor (1845 - 1918) yet, and everybody was

happy. You don't need the set builder to deal algebraically
with equations. Where would you need it?

Mild Shock schrieb am Sonntag, 13. August 2023 um 12:30:52 UTC+2:
> In as far Category Theory and subsequently Categorical Logic
> has some therapeutic value. The DNA/RNA example is from here:
>
> Category Theory for the Sciences
> "Application 2.2.1.1. The central dogma of molecular
> biology is that “DNA codes for RNA codes for protein”.
> That is, there is a function from DNA triplets to RNA triplets
> and a function from RNA triplets to amino acids. But
> sometimes we just want to discuss the translation from
> DNA to amino acids, and this is the composite of the other two"
> https://math.mit.edu/~dspivak/CT4S.pdf
>
> Category Theory see everything through the lense of
> function composition. Quite consequently even.
> Mild Shock schrieb am Sonntag, 13. August 2023 um 12:25:28 UTC+2:
> > Fritzy Boy is the same type of crank as here, that would say, this
> > sentence is wrong. "DNA expresses enzymes".
> >
> > And tends to correct you, to the correct thing is: "DNA expresses
> > RNA, and RNA expresses enzymes".
> >
> > Who cares?
> > Fritz Feldhase schrieb am Samstag, 12. August 2023 um 16:34:41 UTC+2:
> > > On Saturday, August 12, 2023 at 2:52:33 PM UTC+2, Mild Shock wrote:
> > >
> > > > This here is an infinite line, not a line segment: a*x + b*y + c = 0
> > > Actually, (strictly speaking) it's not a line, but an equation (specifying a line).
> > >
> > > The corresponding line may be defined as the set {(x, y) e IR x IR : a*x + b*y + c = 0}.
> > > "Every line L (including vertical lines) is the set of all points whose coordinates (x, y) satisfy a linear equation; that is,
> > > L = {(x, y) : ax + by = c},
> > >
> > > where a, b and c are fixed real numbers (called coefficients) such that a and b are not both zero." (Wikipedia)

On Sunday, 13 August 2023 at 06:38:44 UTC-4, Mild Shock wrote:
> The idea to require that we turn an equation:
> a*x + b*y + c = 0
> Into a set of pairs:
> {(x, y) e IR x IR : a*x + b*y + c = 0}
> Is also a sign of a certain brain wash. Who says
> that every Category Cat must end in the Category Set?
> Are there Categories Cat that are not mappable to
>
> the Category Set? Historically, if we locate Algebraic
> Geometry with Rene Descartes (1596 - 1650), there was
> no Georg Cantor (1845 - 1918) yet, and everybody was
>
> happy. You don't need the set builder to deal algebraically
> with equations. Where would you need it?
> Mild Shock schrieb am Sonntag, 13. August 2023 um 12:30:52 UTC+2:
> > In as far Category Theory and subsequently Categorical Logic
> > has some therapeutic value. The DNA/RNA example is from here:
> >
> > Category Theory for the Sciences
> > "Application 2.2.1.1. The central dogma of molecular
> > biology is that “DNA codes for RNA codes for protein”.
> > That is, there is a function from DNA triplets to RNA triplets
> > and a function from RNA triplets to amino acids. But
> > sometimes we just want to discuss the translation from
> > DNA to amino acids, and this is the composite of the other two"
> > https://math.mit.edu/~dspivak/CT4S.pdf
> >
> > Category Theory see everything through the lense of
> > function composition. Quite consequently even.
> > Mild Shock schrieb am Sonntag, 13. August 2023 um 12:25:28 UTC+2:
> > > Fritzy Boy is the same type of crank as here, that would say, this
> > > sentence is wrong. "DNA expresses enzymes".
> > >
> > > And tends to correct you, to the correct thing is: "DNA expresses
> > > RNA, and RNA expresses enzymes".
> > >
> > > Who cares?
> > > Fritz Feldhase schrieb am Samstag, 12. August 2023 um 16:34:41 UTC+2:
> > > > On Saturday, August 12, 2023 at 2:52:33 PM UTC+2, Mild Shock wrote:
> > > >
> > > > > This here is an infinite line, not a line segment: a*x + b*y + c = 0
> > > > Actually, (strictly speaking) it's not a line, but an equation (specifying a line).
> > > >
> > > > The corresponding line may be defined as the set {(x, y) e IR x IR : a*x + b*y + c = 0}.
> > > > "Every line L (including vertical lines) is the set of all points whose coordinates (x, y) satisfy a linear equation; that is,
> > > > L = {(x, y) : ax + by = c},
> > > >
> > > > where a, b and c are fixed real numbers (called coefficients) such that a and b are not both zero." (Wikipedia)

Well, you don't need set theory at all and thankfully the Ancient Greeks didn't have shit for brains like their descendants the modern Greeks who are nothing but brainwashed little Western College parrots.

Well you are also brainwashed John Gabriel.
Geogebra brainwashed, you cant live without it.
Mostlikely you don't know how to use ruler and compass.

But morons like John Gabriel cannot explain "what"
works as well. And how it nevertheless relates to Set
Theory as well. Category Theory does a quite good job.

Interestingly Rene Descartes math work was in constructive
logic, before the modern version of constructive logic. His
point of departure might have been indeed the Greeks:

"The ancients stated that there are three kinds of geometrical
problems, and that some are called plane, others solid, and
others line-like; and those that can be solved by straight
lines and the circumference of a circle are rightly called plane
because the lines by means of which these problems are
solved have their origin in the plane. But such problems that
must be solved by assuming one or more conic sections in
the construction, are called solid because for their construction
it is necessary to use the surfaces of solid figures, namely cones.
There remains a third kind that is called line-like. For in their
construction other lines than the ones just mentioned are assumed,
having an inconstant and changeable origin, such as spirals, and
the curves that the Greeks call tetragonizousas [“square-making”],
and which we call “quandrantes,” and conchoids, and cissoids,
which have many amazing properties (Pappus 1588, III, §7;
translation from Bos 2001, 38)."
https://plato.stanford.edu/entries/descartes-mathematics/

Eram semper recta schrieb am Sonntag, 13. August 2023 um 14:09:42 UTC+2:
> On Sunday, 13 August 2023 at 06:38:44 UTC-4, Mild Shock wrote:
> > The idea to require that we turn an equation:
> > a*x + b*y + c = 0
> > Into a set of pairs:
> > {(x, y) e IR x IR : a*x + b*y + c = 0}
> > Is also a sign of a certain brain wash. Who says
> > that every Category Cat must end in the Category Set?
> > Are there Categories Cat that are not mappable to
> >
> > the Category Set? Historically, if we locate Algebraic
> > Geometry with Rene Descartes (1596 - 1650), there was
> > no Georg Cantor (1845 - 1918) yet, and everybody was
> >
> > happy. You don't need the set builder to deal algebraically
> > with equations. Where would you need it?
> > Mild Shock schrieb am Sonntag, 13. August 2023 um 12:30:52 UTC+2:
> > > In as far Category Theory and subsequently Categorical Logic
> > > has some therapeutic value. The DNA/RNA example is from here:
> > >
> > > Category Theory for the Sciences
> > > "Application 2.2.1.1. The central dogma of molecular
> > > biology is that “DNA codes for RNA codes for protein”..
> > > That is, there is a function from DNA triplets to RNA triplets
> > > and a function from RNA triplets to amino acids. But
> > > sometimes we just want to discuss the translation from
> > > DNA to amino acids, and this is the composite of the other two"
> > > https://math.mit.edu/~dspivak/CT4S.pdf
> > >
> > > Category Theory see everything through the lense of
> > > function composition. Quite consequently even.
> > > Mild Shock schrieb am Sonntag, 13. August 2023 um 12:25:28 UTC+2:
> > > > Fritzy Boy is the same type of crank as here, that would say, this
> > > > sentence is wrong. "DNA expresses enzymes".
> > > >
> > > > And tends to correct you, to the correct thing is: "DNA expresses
> > > > RNA, and RNA expresses enzymes".
> > > >
> > > > Who cares?
> > > > Fritz Feldhase schrieb am Samstag, 12. August 2023 um 16:34:41 UTC+2:
> > > > > On Saturday, August 12, 2023 at 2:52:33 PM UTC+2, Mild Shock wrote:
> > > > >
> > > > > > This here is an infinite line, not a line segment: a*x + b*y + c = 0
> > > > > Actually, (strictly speaking) it's not a line, but an equation (specifying a line).
> > > > >
> > > > > The corresponding line may be defined as the set {(x, y) e IR x IR : a*x + b*y + c = 0}.
> > > > > "Every line L (including vertical lines) is the set of all points whose coordinates (x, y) satisfy a linear equation; that is,
> > > > > L = {(x, y) : ax + by = c},
> > > > >
> > > > > where a, b and c are fixed real numbers (called coefficients) such that a and b are not both zero." (Wikipedia)
> Well, you don't need set theory at all and thankfully the Ancient Greeks didn't have shit for brains like their descendants the modern Greeks who are nothing but brainwashed little Western College parrots.

And then it happend that he recasts constructive logic,
The most famous letter written to Beeckman in 1619
dates from 26 March of that year. In this letter Descartes

announces his plan to expound an “entirely new
science [scientia penitus nova]. He has an idea of
new compases, which is described as follows:

"So also I hope to show for continuous quantities
that some problems can be solved by straight lines
and circles alone; others only by other curved lines,
which, however, result from a single motion and can
therefore be drawn with new types of compasses,
which are no less exact and geometrical, I think, than
the common ones used to draw circles; and finally
others that can be solved by curved lines generated by
diverse motions not subordinated to one another,
which curves are certainly only imaginary such as the
rather well-known quadratrix."
https://plato.stanford.edu/entries/descartes-mathematics/

Mild Shock schrieb am Sonntag, 13. August 2023 um 16:10:56 UTC+2:
> Well you are also brainwashed John Gabriel.
> Geogebra brainwashed, you cant live without it.
> Mostlikely you don't know how to use ruler and compass.
>
> But morons like John Gabriel cannot explain "what"
> works as well. And how it nevertheless relates to Set
> Theory as well. Category Theory does a quite good job.
>
> Interestingly Rene Descartes math work was in constructive
> logic, before the modern version of constructive logic. His
> point of departure might have been indeed the Greeks:
>
> "The ancients stated that there are three kinds of geometrical
> problems, and that some are called plane, others solid, and
> others line-like; and those that can be solved by straight
> lines and the circumference of a circle are rightly called plane
> because the lines by means of which these problems are
> solved have their origin in the plane. But such problems that
> must be solved by assuming one or more conic sections in
> the construction, are called solid because for their construction
> it is necessary to use the surfaces of solid figures, namely cones.
> There remains a third kind that is called line-like. For in their
> construction other lines than the ones just mentioned are assumed,
> having an inconstant and changeable origin, such as spirals, and
> the curves that the Greeks call tetragonizousas [“square-making”],
> and which we call “quandrantes,” and conchoids, and cissoids,
> which have many amazing properties (Pappus 1588, III, §7;
> translation from Bos 2001, 38)."
> https://plato.stanford.edu/entries/descartes-mathematics/
> Eram semper recta schrieb am Sonntag, 13. August 2023 um 14:09:42 UTC+2:
> > On Sunday, 13 August 2023 at 06:38:44 UTC-4, Mild Shock wrote:
> > > The idea to require that we turn an equation:
> > > a*x + b*y + c = 0
> > > Into a set of pairs:
> > > {(x, y) e IR x IR : a*x + b*y + c = 0}
> > > Is also a sign of a certain brain wash. Who says
> > > that every Category Cat must end in the Category Set?
> > > Are there Categories Cat that are not mappable to
> > >
> > > the Category Set? Historically, if we locate Algebraic
> > > Geometry with Rene Descartes (1596 - 1650), there was
> > > no Georg Cantor (1845 - 1918) yet, and everybody was
> > >
> > > happy. You don't need the set builder to deal algebraically
> > > with equations. Where would you need it?
> > > Mild Shock schrieb am Sonntag, 13. August 2023 um 12:30:52 UTC+2:
> > > > In as far Category Theory and subsequently Categorical Logic
> > > > has some therapeutic value. The DNA/RNA example is from here:
> > > >
> > > > Category Theory for the Sciences
> > > > "Application 2.2.1.1. The central dogma of molecular
> > > > biology is that “DNA codes for RNA codes for protein”.
> > > > That is, there is a function from DNA triplets to RNA triplets
> > > > and a function from RNA triplets to amino acids. But
> > > > sometimes we just want to discuss the translation from
> > > > DNA to amino acids, and this is the composite of the other two"
> > > > https://math.mit.edu/~dspivak/CT4S.pdf
> > > >
> > > > Category Theory see everything through the lense of
> > > > function composition. Quite consequently even.
> > > > Mild Shock schrieb am Sonntag, 13. August 2023 um 12:25:28 UTC+2:
> > > > > Fritzy Boy is the same type of crank as here, that would say, this
> > > > > sentence is wrong. "DNA expresses enzymes".
> > > > >
> > > > > And tends to correct you, to the correct thing is: "DNA expresses
> > > > > RNA, and RNA expresses enzymes".
> > > > >
> > > > > Who cares?
> > > > > Fritz Feldhase schrieb am Samstag, 12. August 2023 um 16:34:41 UTC+2:
> > > > > > On Saturday, August 12, 2023 at 2:52:33 PM UTC+2, Mild Shock wrote:
> > > > > >
> > > > > > > This here is an infinite line, not a line segment: a*x + b*y + c = 0
> > > > > > Actually, (strictly speaking) it's not a line, but an equation (specifying a line).
> > > > > >
> > > > > > The corresponding line may be defined as the set {(x, y) e IR x IR : a*x + b*y + c = 0}.
> > > > > > "Every line L (including vertical lines) is the set of all points whose coordinates (x, y) satisfy a linear equation; that is,
> > > > > > L = {(x, y) : ax + by = c},
> > > > > >
> > > > > > where a, b and c are fixed real numbers (called coefficients) such that a and b are not both zero." (Wikipedia)
> > Well, you don't need set theory at all and thankfully the Ancient Greeks didn't have shit for brains like their descendants the modern Greeks who are nothing but brainwashed little Western College parrots.

Did he need the concept that a curve is a set of points?
Not necessarely. If we view the idea of "single motion"
defining a curve, we might see a finite length curve c in

the plane more holistically as simply a pair of functions:

c_x : [0,1] -> R, c_y : [0,1] -> R

a finite length curve c and even its graph, might be seen
as a pair of function, whith speaking of sets of points. But
functions is also all there is in Category Theory.

This is not to say that the concept of point didn't exist.
His new compases require of curse the drawing of two
curves, and then assuming that we can further proceed

with the intersection of these curves, the points that result
of intersecting curves. So if there are two finite length curves
c and d, in constructive logic the points that are on both

curves are somehow assumed to be end products or
byproducts in a construction.

Mild Shock schrieb am Sonntag, 13. August 2023 um 16:14:21 UTC+2:
> And then it happend that he recasts constructive logic,
> The most famous letter written to Beeckman in 1619
> dates from 26 March of that year. In this letter Descartes
>
> announces his plan to expound an “entirely new
> science [scientia penitus nova]. He has an idea of
> new compases, which is described as follows:
>
> "So also I hope to show for continuous quantities
> that some problems can be solved by straight lines
> and circles alone; others only by other curved lines,
> which, however, result from a single motion and can
> therefore be drawn with new types of compasses,
> which are no less exact and geometrical, I think, than
> the common ones used to draw circles; and finally
> others that can be solved by curved lines generated by
> diverse motions not subordinated to one another,
> which curves are certainly only imaginary such as the
> rather well-known quadratrix."
> https://plato.stanford.edu/entries/descartes-mathematics/
> Mild Shock schrieb am Sonntag, 13. August 2023 um 16:10:56 UTC+2:
> > Well you are also brainwashed John Gabriel.
> > Geogebra brainwashed, you cant live without it.
> > Mostlikely you don't know how to use ruler and compass.
> >
> > But morons like John Gabriel cannot explain "what"
> > works as well. And how it nevertheless relates to Set
> > Theory as well. Category Theory does a quite good job.
> >
> > Interestingly Rene Descartes math work was in constructive
> > logic, before the modern version of constructive logic. His
> > point of departure might have been indeed the Greeks:
> >
> > "The ancients stated that there are three kinds of geometrical
> > problems, and that some are called plane, others solid, and
> > others line-like; and those that can be solved by straight
> > lines and the circumference of a circle are rightly called plane
> > because the lines by means of which these problems are
> > solved have their origin in the plane. But such problems that
> > must be solved by assuming one or more conic sections in
> > the construction, are called solid because for their construction
> > it is necessary to use the surfaces of solid figures, namely cones.
> > There remains a third kind that is called line-like. For in their
> > construction other lines than the ones just mentioned are assumed,
> > having an inconstant and changeable origin, such as spirals, and
> > the curves that the Greeks call tetragonizousas [“square-making”],
> > and which we call “quandrantes,” and conchoids, and cissoids,
> > which have many amazing properties (Pappus 1588, III, §7;
> > translation from Bos 2001, 38)."
> > https://plato.stanford.edu/entries/descartes-mathematics/
> > Eram semper recta schrieb am Sonntag, 13. August 2023 um 14:09:42 UTC+2:
> > > On Sunday, 13 August 2023 at 06:38:44 UTC-4, Mild Shock wrote:
> > > > The idea to require that we turn an equation:
> > > > a*x + b*y + c = 0
> > > > Into a set of pairs:
> > > > {(x, y) e IR x IR : a*x + b*y + c = 0}
> > > > Is also a sign of a certain brain wash. Who says
> > > > that every Category Cat must end in the Category Set?
> > > > Are there Categories Cat that are not mappable to
> > > >
> > > > the Category Set? Historically, if we locate Algebraic
> > > > Geometry with Rene Descartes (1596 - 1650), there was
> > > > no Georg Cantor (1845 - 1918) yet, and everybody was
> > > >
> > > > happy. You don't need the set builder to deal algebraically
> > > > with equations. Where would you need it?
> > > > Mild Shock schrieb am Sonntag, 13. August 2023 um 12:30:52 UTC+2:
> > > > > In as far Category Theory and subsequently Categorical Logic
> > > > > has some therapeutic value. The DNA/RNA example is from here:
> > > > >
> > > > > Category Theory for the Sciences
> > > > > "Application 2.2.1.1. The central dogma of molecular
> > > > > biology is that “DNA codes for RNA codes for protein”.
> > > > > That is, there is a function from DNA triplets to RNA triplets
> > > > > and a function from RNA triplets to amino acids. But
> > > > > sometimes we just want to discuss the translation from
> > > > > DNA to amino acids, and this is the composite of the other two"
> > > > > https://math.mit.edu/~dspivak/CT4S.pdf
> > > > >
> > > > > Category Theory see everything through the lense of
> > > > > function composition. Quite consequently even.
> > > > > Mild Shock schrieb am Sonntag, 13. August 2023 um 12:25:28 UTC+2:
> > > > > > Fritzy Boy is the same type of crank as here, that would say, this
> > > > > > sentence is wrong. "DNA expresses enzymes".
> > > > > >
> > > > > > And tends to correct you, to the correct thing is: "DNA expresses
> > > > > > RNA, and RNA expresses enzymes".
> > > > > >
> > > > > > Who cares?
> > > > > > Fritz Feldhase schrieb am Samstag, 12. August 2023 um 16:34:41 UTC+2:
> > > > > > > On Saturday, August 12, 2023 at 2:52:33 PM UTC+2, Mild Shock wrote:
> > > > > > >
> > > > > > > > This here is an infinite line, not a line segment: a*x + b*y + c = 0
> > > > > > > Actually, (strictly speaking) it's not a line, but an equation (specifying a line).
> > > > > > >
> > > > > > > The corresponding line may be defined as the set {(x, y) e IR x IR : a*x + b*y + c = 0}.
> > > > > > > "Every line L (including vertical lines) is the set of all points whose coordinates (x, y) satisfy a linear equation; that is,
> > > > > > > L = {(x, y) : ax + by = c},
> > > > > > >
> > > > > > > where a, b and c are fixed real numbers (called coefficients) such that a and b are not both zero." (Wikipedia)
> > > Well, you don't need set theory at all and thankfully the Ancient Greeks didn't have shit for brains like their descendants the modern Greeks who are nothing but brainwashed little Western College parrots.

torsdag 10 augusti 2023 kl. 00:22:22 UTC+2 skrev Chris M. Thomasson:
> On 7/22/2023 7:40 AM, markus...@gmail.com wrote:
> > lördag 22 juli 2023 kl. 14:23:18 UTC+2 skrev Eram semper recta:
> >> https://www.academia.edu/104816568/How_to_use_a_Chat_Bot_most_effectively_the_number_line
> > A line consists of points. It can be finitely many points or infinitely many points.
> A line to me has two points with infinite points in between them.
>
> p0 and p1, there are infinite points between p0 and p1.
Usually, we define a line as the linear combination of two points (1-t)*a+t*b. In protective space, lines have finitely many points.

If you have two distinct points A=[a0:…:an], B=[b0:…:bn]∈P^n, the corresponding between A and B has its points of the form [u a0+v b0:…:u an+v bn] (u, v∈k, not both zero). A line in projective space associated to a vector space is a plane in that vector space.

In projective geometry any two distinct lines intersect in exactly one point, parallell lines meet in one point at infinity.Tthe line in projective space corresponding to the Euclidean line l on P consists of (1) the points in projective space that correspond to the points on l, and (2) the point at infinity in projective space that is parallel to l.

Crank John Gabriel, aka Eram semper recta wrote:
> On Saturday, 12 August 2023 at 10:34:54 UTC-4, Fritz Feldhase wrote:
>> On Saturday, August 12, 2023 at 2:43:36 PM UTC+2, Eram semper recta wrote:
>>
>>> y = (c - ax)/b and ax + by = c are the SAME equation
>> It's clear that you are suffering from a psyhosis (or some sort of mental breakdown), man.
>
> You are definitely suffering from psychosis because no one will deny that y = (c - ax)/b and ax + by = c are the SAME equation.

Definitely John ! especially if b = 0 !

Seriously John, find another hobby...