On Thursday, 18 August 2022 at 09:31:16 UTC+8, richar...@gmail.com wrote:
> On 8/17/22 8:25 AM, wij wrote:
> > On Wednesday, 17 August 2022 at 20:17:44 UTC+8, richar...@gmail.com wrote:
> >> On 8/17/22 2:34 AM, wij wrote:
> >>>> ...
> >>> It already mentioned: Your math. cannot say "x+1 is closer than x to infinity".
> >>> You often say infinity is a (your?) "concept", what kind of concept?
> >>> Where is your books say infinity is a Special "vaue"?
> >>> Where in your books Infinity/Closer/Approaching is defined?
> >>>
> >>> You cannot use "-∞ <------ 0 ------> +∞" to debate anything.
> >>> You keep dream talking.
> >> I am just following the standard model of the Real Numbers.
> >>
> >> I don't have the time to teach you that.
> >
> > I know, DEFINITION man. The problem is that you don't really know what the
> > standard model and the Real Numbers and DEFINITION you are talking about.
> > It is time to stop dream-talk and accept my proposal.
> The problem is that once you try to define that "infinity - x"
> represents a number, you open the system to contradictions.
>
> It has been shown that trying to make "infinity" act like a number
> REQUIRES the remove of some other "standard" rule of the Real Number
> system that we like to be able to assume.
>
> Thus, there is a sharp line between the Real Number System that doesn't
> include "Infinity" as a number, and the various Trans-Finite system that
> do allow "Infinity" to be treated as a "Normal" member of the system.
>
> One of the big problems is that there are many ways to get to "infinity"
> and if you try to make it work as a normal value, and let "infinity" ==
> "infinity" be true.
>
> For instancd, the sum of the odd Natural numbers is infinity, as is the
> sum of the even Natural numbers, as is the sum of the Natual numbers.
>
> But clearly the sum of the Natural Numbers is the sum of the odd Natural
> Numbers + the Sum of the Even Natural Numbers so
>
> Infinity = Infinity + Infinity.
>
> Subtract an Infinity from both sides and you get:
>
>
> 0 = Infinity.
>
> Which seems crazy. This is what happens when you try to treat "Infinity"
> as just a normal number. You need to remove certain operations, at least
> when some of the operands are an infinite.

It depends. The root reason is your notion of infinity is fuzzy.
That leads to your infinity sometimes means unbounded large, sometimes a normal
value, sometimes not, sometimes just an indication word. When really arguing,
infinity does not exist. Like infinitesimal, at the beginning it is unbounded
small non-zero VALUE, In the end, it is zero VALUE. When arguing, infinitesimal
does not exist. What is the difference with POO Halt !!!

How can we arguing this for a definite answer? No, we cannot.
If we want a definite answer or a number containing infinity/infinitesimal in
its expression definite, make the meaning unique first as I did.

On 8/17/2022 8:47 PM, Richard Damon wrote:
> On 8/17/22 10:28 PM, Jeff Barnett wrote:
>> On 8/17/2022 6:54 PM, Richard Damon wrote:
>>> On 8/17/22 8:23 AM, Skep Dick wrote:
>>>> On Wednesday, 17 August 2022 at 14:15:39 UTC+2, richar...@gmail.com
>>>> wrote:
>>>>> And the model you choose affects what operations are defined on all
>>>>> values.
>>>> And the operations you choose affects the extensibility of your system!
>>>>
>>>>> Nope, that your problem, You can have a comparative order without a
>>>>> metric.
>>>> That's not "my" problem. That's YOUR problem. You want a decidable <
>>>> operator on elements of R.
>>>>
>>>> Shame.
>>>
>>> There IS a decidable < operation on elements of R.
>>>
>>> The fact that "closer to infinity", since infinity isn't a normal
>>> value of the field is defined differently than "closer to x" where x
>>> IS a member of the field isn't a problem.
>>>
>>> That is just operator overloading.
>>>
>>> x is closer to infinity than y if x > y, which holds for all x and y
>>> that are actually members of the Real Number system.
>>
>> What on Earth do you mean closer to infinity?
>>
>> Surely inf - x and inf - y are equal for finite x an y whether they
>> are equal or not. Actually both differences equal inf. If you don't
>> like that, you might say they are incomparable but that probably isn't
>> true.
>
>
> But x and y ARE comparable, and so we know which one if farther in the
> direction towards that which is towards infinity.

No. I was saying that that you might consider inf - x and inf - y
incomparable then I said that probably isn't true.

> We don't need to measure how close somethings are to "The Sky" to tell
> which one is higher, i.e closer to the sky.

The sky is only finite in height. And that is the whole point actually.

> Closer to (positve) infinity thus becomes an equivalent expression to
> larger.
> Note, this definition, which is used in limit theory implies that there
> are two different "Infinite" limits, one to the positive end, and one to
> the negative end, +Inf and -Inf, and closer to +Inf is larger, and
> closer to -Inf is the smaller (more negative, or less positive)

The reals and inf don't work that way. Do you believe that 2 * inf >
inf? That inf - inf = 0? That inf + 1 =/= inf? And so on. Here's another
if you want to go into it: inf (the one that's written as a side wise 8)
is greater or smaller or equal to alpha_0, alpha_1, etc. None of these
things are numbers per se and they do not obey arithmetic rules with
each other or finite numbers.
--
Jeff Barnett

On Wednesday, 17 August 2022 at 23:09:09 UTC+2, dklei...@gmail.com wrote:
> On Wednesday, August 17, 2022 at 12:08:11 AM UTC-7, Skep Dick wrote:
> > On Wednesday, 17 August 2022 at 07:15:58 UTC+2, dklei...@gmail.com wrote:
> > > Once chosen 0 does not change and the isomorphism
> > > stops being of interest.
> > It stops being of interest ??!?!?!
> >
> > -∞<----------------------0-> +∞
> > is isomorphic to
> > -∞<-0----------------------> +∞
> >
> > It gang-rapes my intuition that the isomorphism is being preserved despite my moving the "0" left and right!
> >
> There is a complete continuum of either side of 0. Seems obvious from the meaning of infinity.
Are you actually capable of reading complete English sentences?!? Maybe your cultural/Mathematical biases are getting in your way of understanding me. Lets replace the symbol "0" with the symbol "X". Let x represent a free variable on the continuum.

-∞<-X----------------------> +∞

What does it mean for x to approach -∞; or +-∞ if there is ALWAYS a complete continuum on either side of ANY x ?!?

On Wednesday, 17 August 2022 at 23:14:49 UTC+2, dklei...@gmail.com wrote:
> On Wednesday, August 17, 2022 at 5:04:40 AM UTC-7, Skep Dick wrote:
> > On Wednesday, 17 August 2022 at 13:54:24 UTC+2, richar...@gmail.com wrote:
> > > Why is that a problem, many things that are True are unintuitive.
> > Because Truth in Mathematics is ALWAYS relative to a model!
> >
> > And the model is semantic (intuition!) not syntactic (proofs).
> > > Especially when you throw things like infinity into the mix, as we have
> > > trouble really understanding it.
> > I mean... your first sign of trouble is the ∃ operator. Which one is true?
> >
> > ∃∞ or ¬∃∞ ?
> >
> > And the answer is... whichever model you CHOOSE.
> > > Maybe the biggest part of the issue is you are thinking of infinity
> > > being AT the > symbol, when actually that is telling you it isn't there
> > > but off a REAL FAR DISTANCE in that direction.
> > Maybe your problem is that you think there is a DISTANCE metric to infinity?
> Metrics are a poverty-stricken way to talk about limits. You need a topology.
You are not hearing or understanding a word of English!

I have given you a topology! The continuum itself.

-∞<-------------------------------> +∞

And I have given you a free variable - x.

-∞<-------x----------------------> +∞

Now thell me what lim(x-> +∞); or lim(x -> -∞) means!

On Wednesday, 17 August 2022 at 23:18:26 UTC+2, Alan Mackenzie wrote:
> That's really a troll question, which seems designed to embroil somebody
> knowledgeable in stupid questions like how many angels can stand on the
> head of a pin.
I am not trolling. You are trolling!

> You want a real answer to your question? That is that "infinity" is not
> a real number, and no real number has a distance to "infinity", distance
> being something defined on the real numbers.
>
> I think Richard used the phrase "REAL FAR DISTANCE in that direction" as
> a thinking aid for those not versed in real analysis. It's false, as
> children's fairy tales are "false", but it's a way of getting concepts
> over in an easy to digest fashion.
Maybe if you stopped treating me as a child, and started treating me as somebody at least as smat as you then we could actually have a conversation?

Until you learn some manners, I will speak to you in your own language. That is - I will look down on you.

You idiot.

On Thursday, 18 August 2022 at 09:29:12 UTC+2, Jeff Barnett wrote:
> On 8/17/2022 8:47 PM, Richard Damon wrote:
> > On 8/17/22 10:28 PM, Jeff Barnett wrote:
> >> On 8/17/2022 6:54 PM, Richard Damon wrote:
> >>> On 8/17/22 8:23 AM, Skep Dick wrote:
> >>>> On Wednesday, 17 August 2022 at 14:15:39 UTC+2, richar...@gmail.com
> >>>> wrote:
> >>>>> And the model you choose affects what operations are defined on all
> >>>>> values.
> >>>> And the operations you choose affects the extensibility of your system!
> >>>>
> >>>>> Nope, that your problem, You can have a comparative order without a
> >>>>> metric.
> >>>> That's not "my" problem. That's YOUR problem. You want a decidable <
> >>>> operator on elements of R.
> >>>>
> >>>> Shame.
> >>>
> >>> There IS a decidable < operation on elements of R.
> >>>
> >>> The fact that "closer to infinity", since infinity isn't a normal
> >>> value of the field is defined differently than "closer to x" where x
> >>> IS a member of the field isn't a problem.
> >>>
> >>> That is just operator overloading.
> >>>
> >>> x is closer to infinity than y if x > y, which holds for all x and y
> >>> that are actually members of the Real Number system.
> >>
> >> What on Earth do you mean closer to infinity?
> >>
> >> Surely inf - x and inf - y are equal for finite x an y whether they
> >> are equal or not. Actually both differences equal inf. If you don't
> >> like that, you might say they are incomparable but that probably isn't
> >> true.
> >
> >
> > But x and y ARE comparable, and so we know which one if farther in the
> > direction towards that which is towards infinity.
> No. I was saying that that you might consider inf - x and inf - y
> incomparable then I said that probably isn't true.
> > We don't need to measure how close somethings are to "The Sky" to tell
> > which one is higher, i.e closer to the sky.
> The sky is only finite in height. And that is the whole point actually.
> > Closer to (positve) infinity thus becomes an equivalent expression to
> > larger.
> > Note, this definition, which is used in limit theory implies that there
> > are two different "Infinite" limits, one to the positive end, and one to
> > the negative end, +Inf and -Inf, and closer to +Inf is larger, and
> > closer to -Inf is the smaller (more negative, or less positive)
> The reals and inf don't work that way. Do you believe that 2 * inf >
> inf? That inf - inf = 0? That inf + 1 =/= inf? And so on. Here's another
> if you want to go into it: inf (the one that's written as a side wise 8)
> is greater or smaller or equal to alpha_0, alpha_1, etc. None of these
> things are numbers per se and they do not obey arithmetic rules with
> each other or finite numbers.
Whaaaat the fuuuuck?

Let the cardinality... oh no! I said a bad word.

Let the size (no, I am not going to define it) of the continuum (-∞, +∞) be C (for Continuum!)
For any x on (-∞, +∞):
Let the size of (-∞, x) be L (for Left part of Continuum!)
Let the size of (x, +∞) be R (for Right part of Continuum!)
The size of x is 1.

We can be very honest with ourselves and admit that identifying ANY X on C is exactly the same thing as the / operator because ANY X splits C into two equal parts.

Surely then ALL of these follow (for all of the intuitive/geometric notions of +,-,<, >, =) etc!
1 < R
1 < L
L < C
R < C
R / L = 1
L / R = 1
L = R
0 = L - R
0 = R - L
C - C = R - L
C-R = C-L
C = L + R + 1
C = 2R + 1
C = 2L + 1
C > 2R
C > 2L

Surely one doesn't need anything other than intuition to arrive here (even if there is a theory out there which says the same thing) ?!? But if I had to give it a name - I'd call it projective geometry or something.

Because I (obviously) have a point (OF VIEW). And I am projecting my point (OF VIEW) onto a continuum.
And in the act of CHOOSING a point (on the continuum) and in doing so I am dividing the continuum into two parts.

And thus I have introduced a discontinuity. Ooops!

Axiom of choice. Axiom of continuum discontinuity.

Potato. Potatoh.

On Wednesday, 17 August 2022 at 19:53:41 UTC+2, Alan Mackenzie wrote:
> > Base 2 mathematics for computer scientists.
> > Base 10 for the SI system.
> > Base 60 for the Babylonians.
> > Base 20 for the French
>
> OK, 10 out of 10 for word play, but these ways of counting are not
> radically different. They all use a base, for example.
It's not wordplay, you troll.

You have literally just erased ALL the differences into the abstract concept of a "base".
And from the point of view of "a base" ALL number-systems are now "the same" to you.
And that's PRECISELY how you miss the point. Over-abstraction.

Lets us now use base 0 for our number system.

I have ONE egg in the fridge. This means I have 0 eggs!
I have NO eggs in the fridge. This means I have NO(0)

> They're all part of standard mathematics, such as is taught in degree
> level courses.
And what about base-0 mathematics? Is that also standard?

> Yes, since mathematics is far more difficult without appropriate
> notations. But mathematics consists of a great deal more than mere
> notations.
No it doesn't. It's just syntax.

> This seems not to be the case.
That's only because you (erroneously) believe to be smarter than me.

On Thursday, 18 August 2022 at 11:26:03 UTC+1, Skep Dick wrote:
> On Wednesday, 17 August 2022 at 19:53:41 UTC+2, Alan Mackenzie wrote:
> > > Base 2 mathematics for computer scientists.
> > > Base 10 for the SI system.
> > > Base 60 for the Babylonians.
> > > Base 20 for the French
> >
> > OK, 10 out of 10 for word play, but these ways of counting are not
> > radically different. They all use a base, for example.
> It's not wordplay, you troll.
>
> You have literally just erased ALL the differences into the abstract concept of a "base".
> And from the point of view of "a base" ALL number-systems are now "the same" to you.
> And that's PRECISELY how you miss the point. Over-abstraction.
>
> Lets us now use base 0 for our number system.
>
> I have ONE egg in the fridge. This means I have 0 eggs!
> I have NO eggs in the fridge. This means I have NO(0)
> > They're all part of standard mathematics, such as is taught in degree
> > level courses.
> And what about base-0 mathematics? Is that also standard?
>
0^0 is one
0^1 is zero
0^-1 is infinity

So we can represent some numbers, leaving the question of whether infinity is a number.
Now what symbols are we to use? If we have symbols from 0 to 0 -1, inclusive, then we
have no symbols if we count up. If we say that we are allowed to count down, we have a symbol
for 0 and a symbol for -1.
So we can represent zero, -1 or -infinity in base 0.

On Thursday, 18 August 2022 at 12:40:55 UTC+2, malcolm.ar...@gmail.com wrote:
> So we can represent some numbers, leaving the question of whether infinity is a number.
> Now what symbols are we to use? If we have symbols from 0 to 0 -1, inclusive, then we
> have no symbols if we count up. If we say that we are allowed to count down, we have a symbol
> for 0 and a symbol for -1.
> So we can represent zero, -1 or -infinity in base 0.
What do you mean by "1" in base 0?
Do you mean 0^0 or 00 ?

On Thursday, 18 August 2022 at 11:57:20 UTC+1, Skep Dick wrote:
> On Thursday, 18 August 2022 at 12:40:55 UTC+2, malcolm.ar...@gmail.com wrote:
> > So we can represent some numbers, leaving the question of whether infinity is a number.
> > Now what symbols are we to use? If we have symbols from 0 to 0 -1, inclusive, then we
> > have no symbols if we count up. If we say that we are allowed to count down, we have a symbol
> > for 0 and a symbol for -1.
> > So we can represent zero, -1 or -infinity in base 0.
> What do you mean by "1" in base 0?
> Do you mean 0^0 or 00 ?
>
Decimal
.... 10^-2 10^-1 10^0 10^1 10^2 ....
Binary
....2^-2 2^-1 2^0 2^1 2^2 ...
Base zero
....0^-2 0^-1 0^0 0^1 0^2...

So we have a column for units in base zero.

On Thursday, 18 August 2022 at 13:29:37 UTC+2, malcolm.ar...@gmail.com wrote:
> On Thursday, 18 August 2022 at 11:57:20 UTC+1, Skep Dick wrote:
> > On Thursday, 18 August 2022 at 12:40:55 UTC+2, malcolm.ar...@gmail.com wrote:
> > > So we can represent some numbers, leaving the question of whether infinity is a number.
> > > Now what symbols are we to use? If we have symbols from 0 to 0 -1, inclusive, then we
> > > have no symbols if we count up. If we say that we are allowed to count down, we have a symbol
> > > for 0 and a symbol for -1.
> > > So we can represent zero, -1 or -infinity in base 0.
> > What do you mean by "1" in base 0?
> > Do you mean 0^0 or 00 ?
> >
> Decimal
> ... 10^-2 10^-1 10^0 10^1 10^2 ....
> Binary
> ...2^-2 2^-1 2^0 2^1 2^2 ...
> Base zero
> ...0^-2 0^-1 0^0 0^1 0^2...
>
> So we have a column for units in base zero.
WOWOWOWOW! Slow down, cowboy!

I am talking about the basic, human intuition of counting, MAN!

I have 0 eggs <-> Base10(1) <-> 🥚
I have 00 eggs <-> Base10(2) <-> 🥚🥚
I have 000 eggs <-> Base10(3) <-> 🥚🥚 🥚
I have NO eggs <-> Base10(0) <->

I have no idea what you mean by 🥚 ^ 🥚

Skep Dick <skepdick22@gmail.com> wrote:
> On Wednesday, 17 August 2022 at 23:18:26 UTC+2, Alan Mackenzie wrote:

[ .... ]

>> You want a real answer to your question? That is that "infinity" is not
>> a real number, and no real number has a distance to "infinity", distance
>> being something defined on the real numbers.

>> I think Richard used the phrase "REAL FAR DISTANCE in that direction" as
>> a thinking aid for those not versed in real analysis. It's false, as
>> children's fairy tales are "false", but it's a way of getting concepts
>> over in an easy to digest fashion.

> Maybe if you stopped treating me as a child, and started treating me
> as somebody at least as smart as you then we could actually have a
> conversation?

You want a conversation? You may be as smart as me, whatever that
means, but you are not educated in mathematics to any degree; I am.
Mathematics is the topic of the current thread.

> Until you learn some manners, I will speak to you in your own
> language. That is - I will look down on you.

Manners, eh? To manners belongs respect. If the subject of the thread
were special purpose computer languages, I would respect your special
knowledge on the topic, and wouldn't keep pestering you with stupidities
about the basics.

A number of people in this thread have expertise on mathematics that you
lack. Respect for that expertise is due from you. So far, you haven't
shown any.

> You idiot.

Grow up.

--
Alan Mackenzie (Nuremberg, Germany).

On 8/18/22 3:29 AM, Jeff Barnett wrote:
> On 8/17/2022 8:47 PM, Richard Damon wrote:
>> On 8/17/22 10:28 PM, Jeff Barnett wrote:
>>> On 8/17/2022 6:54 PM, Richard Damon wrote:
>>>> On 8/17/22 8:23 AM, Skep Dick wrote:
>>>>> On Wednesday, 17 August 2022 at 14:15:39 UTC+2, richar...@gmail.com
>>>>> wrote:
>>>>>> And the model you choose affects what operations are defined on
>>>>>> all values.
>>>>> And the operations you choose affects the extensibility of your
>>>>> system!
>>>>>
>>>>>> Nope, that your problem, You can have a comparative order without
>>>>>> a metric.
>>>>> That's not "my" problem. That's YOUR problem. You want a decidable
>>>>> < operator on elements of R.
>>>>>
>>>>> Shame.
>>>>
>>>> There IS a decidable < operation on elements of R.
>>>>
>>>> The fact that "closer to infinity", since infinity isn't a normal
>>>> value of the field is defined differently than "closer to x" where x
>>>> IS a member of the field isn't a problem.
>>>>
>>>> That is just operator overloading.
>>>>
>>>> x is closer to infinity than y if x > y, which holds for all x and y
>>>> that are actually members of the Real Number system.
>>>
>>> What on Earth do you mean closer to infinity?
>>>
>>> Surely inf - x and inf - y are equal for finite x an y whether they
>>> are equal or not. Actually both differences equal inf. If you don't
>>> like that, you might say they are incomparable but that probably
>>> isn't true.
>>
>>
>> But x and y ARE comparable, and so we know which one if farther in the
>> direction towards that which is towards infinity.
>
> No. I was saying that that you might consider inf - x and inf - y
> incomparable then I said that probably isn't true.

No, you tried to make inf - x an "legal" value. The problem is that in
The Real Number System, you can't do that, inf isn't a "value" so you
can't do math on it.

>
>> We don't need to measure how close somethings are to "The Sky" to tell
>> which one is higher, i.e closer to the sky.
>
> The sky is only finite in height. And that is the whole point actually.

Really? Where is the edge of th sky. I see stars up in the sky, those
are REAL far away. It it high enough to make a reasonable analogy, even
if not perfec.

>
>> Closer to (positve) infinity thus becomes an equivalent expression to
>> larger.
>> Note, this definition, which is used in limit theory implies that
>> there are two different "Infinite" limits, one to the positive end,
>> and one to the negative end, +Inf and -Inf, and closer to +Inf is
>> larger, and closer to -Inf is the smaller (more negative, or less
>> positive)
>
> The reals and inf don't work that way. Do you believe that 2 * inf >
> inf? That inf - inf = 0? That inf + 1 =/= inf? And so on. Here's another
> if you want to go into it: inf (the one that's written as a side wise 8)
> is greater or smaller or equal to alpha_0, alpha_1, etc. None of these
> things are numbers per se and they do not obey arithmetic rules with
> each other or finite numbers.

Where did I say 2 * inf > inf, or do any of that math with infinity and
claim it to be correct. That is the sort of thing I say when I am
pointing out the error in trying to make infinity a "Number" just like
the rest.

And yes, when you get to the Aleph (not Alpha) series of infinities, we
get some distinctions between things we call infinity, but all of that
is still outside of The Real Number System, and all fall into the
general concept of we can take a limit as x goes "to infinity".

Skep Dick <skepdick22@gmail.com> wrote:
> On Wednesday, 17 August 2022 at 19:53:41 UTC+2, Alan Mackenzie wrote:
>> > Base 2 mathematics for computer scientists.
>> > Base 10 for the SI system.
>> > Base 60 for the Babylonians.
>> > Base 20 for the French

>> OK, 10 out of 10 for word play, but these ways of counting are not
>> radically different. They all use a base, for example.
> It's not wordplay, you troll.

That went straight over your head, it would seem.

> You have literally just erased ALL the differences into the abstract
> concept of a "base". And from the point of view of "a base" ALL
> number-systems are now "the same" to you. And that's PRECISELY how you
> miss the point. Over-abstraction.

I think it's more like maybe you're not capable of working with high
levels of abstractions. If you can't even see what the systems above
have in common. Maybe if you could have pointed out a culture where the
number system didn't use a base, you might have had a point.

> Lets us now use base 0 for our number system.

That is just silly. Zero is not a suitable base for a number system.
Neither is one.

[ .... ]

>> They're all part of standard mathematics, such as is taught in degree
>> level courses.
> And what about base-0 mathematics? Is that also standard?

No, it's silly.

>> Yes, since mathematics is far more difficult without appropriate
>> notations. But mathematics consists of a great deal more than mere
>> notations.
> No it doesn't. It's just syntax.

Here's where you should show a bit of respect for those that have
expertise you lack.

[ .... ]

--
Alan Mackenzie (Nuremberg, Germany).

On Thursday, 18 August 2022 at 13:45:43 UTC+2, Alan Mackenzie wrote:
> You want a conversation? You may be as smart as me, whatever that
> means, but you are not educated in mathematics to any degree; I am.
Hahahahahaha! Translation in English.

"I am smarter about Mathematics than you are"

You fucking idiot.

> Manners, eh? To manners belongs respect.
It's difficult to respect anyone who equates education with understanding.

>If the subject of the thread were special purpose computer languages
Special purpose computer languages is PRECISELY the subject of the thread!

That is what Mathematics IS! A special-purpose language. Used by computers (a.k.a HUMANS).

A "special purpose computer language" is also known as a FORMAL LANGUAGE.

>I would respect your special knowledge on the topic, and wouldn't keep pestering you with stupidities
> about the basics.
"The basics" of Mathematics are computer science! You fucking idiot.

> A number of people in this thread have expertise on mathematics that you
> lack. Respect for that expertise is due from you. So far, you haven't
> shown any.
My expertise in computer science trumps your "expertise" in Mathematics.

You fucking idiot.

> Grow up.
I am all grown up. But... to manners belong respect.

No respect from you - no manners from me.

On 8/18/22 5:55 AM, Skep Dick wrote:
> On Thursday, 18 August 2022 at 09:29:12 UTC+2, Jeff Barnett wrote:
>> On 8/17/2022 8:47 PM, Richard Damon wrote:
>>> On 8/17/22 10:28 PM, Jeff Barnett wrote:
>>>> On 8/17/2022 6:54 PM, Richard Damon wrote:
>>>>> On 8/17/22 8:23 AM, Skep Dick wrote:
>>>>>> On Wednesday, 17 August 2022 at 14:15:39 UTC+2, richar...@gmail.com
>>>>>> wrote:
>>>>>>> And the model you choose affects what operations are defined on all
>>>>>>> values.
>>>>>> And the operations you choose affects the extensibility of your system!
>>>>>>
>>>>>>> Nope, that your problem, You can have a comparative order without a
>>>>>>> metric.
>>>>>> That's not "my" problem. That's YOUR problem. You want a decidable <
>>>>>> operator on elements of R.
>>>>>>
>>>>>> Shame.
>>>>>
>>>>> There IS a decidable < operation on elements of R.
>>>>>
>>>>> The fact that "closer to infinity", since infinity isn't a normal
>>>>> value of the field is defined differently than "closer to x" where x
>>>>> IS a member of the field isn't a problem.
>>>>>
>>>>> That is just operator overloading.
>>>>>
>>>>> x is closer to infinity than y if x > y, which holds for all x and y
>>>>> that are actually members of the Real Number system.
>>>>
>>>> What on Earth do you mean closer to infinity?
>>>>
>>>> Surely inf - x and inf - y are equal for finite x an y whether they
>>>> are equal or not. Actually both differences equal inf. If you don't
>>>> like that, you might say they are incomparable but that probably isn't
>>>> true.
>>>
>>>
>>> But x and y ARE comparable, and so we know which one if farther in the
>>> direction towards that which is towards infinity.
>> No. I was saying that that you might consider inf - x and inf - y
>> incomparable then I said that probably isn't true.
>>> We don't need to measure how close somethings are to "The Sky" to tell
>>> which one is higher, i.e closer to the sky.
>> The sky is only finite in height. And that is the whole point actually.
>>> Closer to (positve) infinity thus becomes an equivalent expression to
>>> larger.
>>> Note, this definition, which is used in limit theory implies that there
>>> are two different "Infinite" limits, one to the positive end, and one to
>>> the negative end, +Inf and -Inf, and closer to +Inf is larger, and
>>> closer to -Inf is the smaller (more negative, or less positive)
>> The reals and inf don't work that way. Do you believe that 2 * inf >
>> inf? That inf - inf = 0? That inf + 1 =/= inf? And so on. Here's another
>> if you want to go into it: inf (the one that's written as a side wise 8)
>> is greater or smaller or equal to alpha_0, alpha_1, etc. None of these
>> things are numbers per se and they do not obey arithmetic rules with
>> each other or finite numbers.
> Whaaaat the fuuuuck?
>
> Let the cardinality... oh no! I said a bad word.
>
> Let the size (no, I am not going to define it) of the continuum (-∞, +∞) be C (for Continuum!)

(And refusing to define what you means, means your statement is
meaningless).

> For any x on (-∞, +∞):
> Let the size of (-∞, x) be L (for Left part of Continuum!)
> Let the size of (x, +∞) be R (for Right part of Continuum!)
> The size of x is 1.
>
> We can be very honest with ourselves and admit that identifying ANY X on C is exactly the same thing as the / operator because ANY X splits C into two equal parts.
>
> Surely then ALL of these follow (for all of the intuitive/geometric notions of +,-,<, >, =) etc!
> 1 < R
> 1 < L
> L < C
> R < C
> R / L = 1
> L / R = 1
> L = R
> 0 = L - R
> 0 = R - L
> C - C = R - L
> C-R = C-L
> C = L + R + 1
> C = 2R + 1
> C = 2L + 1
> C > 2R
> C > 2L
>
> Surely one doesn't need anything other than intuition to arrive here (even if there is a theory out there which says the same thing) ?!? But if I had to give it a name - I'd call it projective geometry or something.
>
> Because I (obviously) have a point (OF VIEW). And I am projecting my point (OF VIEW) onto a continuum.
> And in the act of CHOOSING a point (on the continuum) and in doing so I am dividing the continuum into two parts.
>
> And thus I have introduced a discontinuity. Ooops!
>
> Axiom of choice. Axiom of continuum discontinuity.
>
> Potato. Potatoh.

Yep, YOU are the discontinuity, and show you don't understand the math
you are spouting.

On 8/18/22 3:56 AM, Skep Dick wrote:
> On Wednesday, 17 August 2022 at 23:14:49 UTC+2, dklei...@gmail.com wrote:
>> On Wednesday, August 17, 2022 at 5:04:40 AM UTC-7, Skep Dick wrote:
>>> On Wednesday, 17 August 2022 at 13:54:24 UTC+2, richar...@gmail.com wrote:
>>>> Why is that a problem, many things that are True are unintuitive.
>>> Because Truth in Mathematics is ALWAYS relative to a model!
>>>
>>> And the model is semantic (intuition!) not syntactic (proofs).
>>>> Especially when you throw things like infinity into the mix, as we have
>>>> trouble really understanding it.
>>> I mean... your first sign of trouble is the ∃ operator. Which one is true?
>>>
>>> ∃∞ or ¬∃∞ ?
>>>
>>> And the answer is... whichever model you CHOOSE.
>>>> Maybe the biggest part of the issue is you are thinking of infinity
>>>> being AT the > symbol, when actually that is telling you it isn't there
>>>> but off a REAL FAR DISTANCE in that direction.
>>> Maybe your problem is that you think there is a DISTANCE metric to infinity?
>> Metrics are a poverty-stricken way to talk about limits. You need a topology.
> You are not hearing or understanding a word of English!
>
> I have given you a topology! The continuum itself.
>
> -∞<-------------------------------> +∞
>
> And I have given you a free variable - x.
>
> -∞<-------x----------------------> +∞
>
> Now thell me what lim(x-> +∞); or lim(x -> -∞) means!
>
>
>

Nothing.

lim, as an operator, needs a function to apply to.

What is "1 + " mean?

On 8/18/22 6:26 AM, Skep Dick wrote:
> On Wednesday, 17 August 2022 at 19:53:41 UTC+2, Alan Mackenzie wrote:
>>> Base 2 mathematics for computer scientists.
>>> Base 10 for the SI system.
>>> Base 60 for the Babylonians.
>>> Base 20 for the French
>>
>> OK, 10 out of 10 for word play, but these ways of counting are not
>> radically different. They all use a base, for example.
> It's not wordplay, you troll.
>
> You have literally just erased ALL the differences into the abstract concept of a "base".
> And from the point of view of "a base" ALL number-systems are now "the same" to you.
> And that's PRECISELY how you miss the point. Over-abstraction.
>
> Lets us now use base 0 for our number system.
>
> I have ONE egg in the fridge. This means I have 0 eggs!
> I have NO eggs in the fridge. This means I have NO(0)
>
>> They're all part of standard mathematics, such as is taught in degree
>> level courses.
> And what about base-0 mathematics? Is that also standard?
>
>> Yes, since mathematics is far more difficult without appropriate
>> notations. But mathematics consists of a great deal more than mere
>> notations.
> No it doesn't. It's just syntax.
>
>> This seems not to be the case.
> That's only because you (erroneously) believe to be smarter than me.

No, I think that is likely, as you prove you are dumber that others.

On 8/18/22 12:36 AM, wij wrote:
> On Thursday, 18 August 2022 at 09:31:16 UTC+8, richar...@gmail.com wrote:
>> On 8/17/22 8:25 AM, wij wrote:
>>> On Wednesday, 17 August 2022 at 20:17:44 UTC+8, richar...@gmail.com wrote:
>>>> On 8/17/22 2:34 AM, wij wrote:
>>>>>> ...
>>>>> It already mentioned: Your math. cannot say "x+1 is closer than x to infinity".
>>>>> You often say infinity is a (your?) "concept", what kind of concept?
>>>>> Where is your books say infinity is a Special "vaue"?
>>>>> Where in your books Infinity/Closer/Approaching is defined?
>>>>>
>>>>> You cannot use "-∞ <------ 0 ------> +∞" to debate anything.
>>>>> You keep dream talking.
>>>> I am just following the standard model of the Real Numbers.
>>>>
>>>> I don't have the time to teach you that.
>>>
>>> I know, DEFINITION man. The problem is that you don't really know what the
>>> standard model and the Real Numbers and DEFINITION you are talking about.
>>> It is time to stop dream-talk and accept my proposal.
>> The problem is that once you try to define that "infinity - x"
>> represents a number, you open the system to contradictions.
>>
>> It has been shown that trying to make "infinity" act like a number
>> REQUIRES the remove of some other "standard" rule of the Real Number
>> system that we like to be able to assume.
>>
>> Thus, there is a sharp line between the Real Number System that doesn't
>> include "Infinity" as a number, and the various Trans-Finite system that
>> do allow "Infinity" to be treated as a "Normal" member of the system.
>>
>> One of the big problems is that there are many ways to get to "infinity"
>> and if you try to make it work as a normal value, and let "infinity" ==
>> "infinity" be true.
>>
>> For instancd, the sum of the odd Natural numbers is infinity, as is the
>> sum of the even Natural numbers, as is the sum of the Natual numbers.
>>
>> But clearly the sum of the Natural Numbers is the sum of the odd Natural
>> Numbers + the Sum of the Even Natural Numbers so
>>
>> Infinity = Infinity + Infinity.
>>
>> Subtract an Infinity from both sides and you get:
>>
>>
>> 0 = Infinity.
>>
>> Which seems crazy. This is what happens when you try to treat "Infinity"
>> as just a normal number. You need to remove certain operations, at least
>> when some of the operands are an infinite.
>
> It depends. The root reason is your notion of infinity is fuzzy.
> That leads to your infinity sometimes means unbounded large, sometimes a normal
> value, sometimes not, sometimes just an indication word. When really arguing,
> infinity does not exist. Like infinitesimal, at the beginning it is unbounded
> small non-zero VALUE, In the end, it is zero VALUE. When arguing, infinitesimal
> does not exist. What is the difference with POO Halt !!!
>
> How can we arguing this for a definite answer? No, we cannot.
> If we want a definite answer or a number containing infinity/infinitesimal in
> its expression definite, make the meaning unique first as I did.

No, in the Real Number System "Infinity" is NEVER a "Normal Value".

THe key is that whenever you talk about something, you need to start by
agreeing on the system you are talking about.

You confusion stems from the fact that many people mix the various
number systems and don't make it clear which thay are talking in.

Yes, if you take a word out of context, by not establishing which system
you are talking about, you get that sort of confusion.

Sort of like if you hear someone say "Nine", you think of the number,
but it might be a German saying "No" (since you can't "hear" the spelling).

The word "Infinity" can mean somewhat different things depending on the
"Language" you are talking in, so knowing the language being spoken can
be important.

On 8/18/22 7:59 AM, Skep Dick wrote:
> On Thursday, 18 August 2022 at 13:45:43 UTC+2, Alan Mackenzie wrote:
>> You want a conversation? You may be as smart as me, whatever that
>> means, but you are not educated in mathematics to any degree; I am.
> Hahahahahaha! Translation in English.
>
> "I am smarter about Mathematics than you are"
>
> You fucking idiot.
>
>> Manners, eh? To manners belongs respect.
> It's difficult to respect anyone who equates education with understanding.
>
>> If the subject of the thread were special purpose computer languages
> Special purpose computer languages is PRECISELY the subject of the thread!
>
> That is what Mathematics IS! A special-purpose language. Used by computers (a.k.a HUMANS).

And if you think Humans are computers you think too little of yourself.

>
> A "special purpose computer language" is also known as a FORMAL LANGUAGE.
>
>> I would respect your special knowledge on the topic, and wouldn't keep pestering you with stupidities
>> about the basics.
> "The basics" of Mathematics are computer science! You fucking idiot.

Hard to make that point when Mathematics vastly predate Computers.

What Computer did Pythagoras use to make his proofs?

>
>> A number of people in this thread have expertise on mathematics that you
>> lack. Respect for that expertise is due from you. So far, you haven't
>> shown any.
> My expertise in computer science trumps your "expertise" in Mathematics.

I don't think you actually understand computer science either.

>
> You fucking idiot.
>
>> Grow up.
> I am all grown up. But... to manners belong respect.
>
> No respect from you - no manners from me.

On Thursday, 18 August 2022 at 13:59:34 UTC+2, Alan Mackenzie wrote:
> That went straight over your head, it would seem.
It went just below my head actually.

Which is why I keep calling you an idiot.

> I think it's more like maybe you're not capable of working with high
> levels of abstractions.
Seeming as you can't even tell he difference between abstraction and over-abstraction, I guess I am more capable than you. Despite your education.

You have absolutely no idea how to count in base 0, do you?

>If you can't even see what the systems above have in common.
Q.E.D ALL you can see is commonality. You fail to see DIFFERENCE.

You are absolutely blind to your own over-abstraction!

>Maybe if you could have pointed out a culture where the
> number system didn't use a base, you might have had a point.
You fucking idiot. I am pointing out THAT moderm Mathematics is base-0 counting!

Which is utterly and ENTIRELY different from (and ignorant about) ALL systems which didn't even have the concept of 0!

> That is just silly. Zero is not a suitable base for a number system.
> Neither is one.
Says who? The idiot?

0 = 1 = 🥚
00 = 11 = 🥚🥚
000 = 111 =🥚🥚🥚
0000 = 1111 = 🥚🥚🥚🥚

> > And what about base-0 mathematics? Is that also standard?
> No, it's silly.
So ALL Mathematics before the concept of zero are silly to you?!?

Idiot.

> Here's where you should show a bit of respect for those that have
> expertise you lack.
There you are. Appealing to the authority of your own "expertise" again.

You over-educated, over-abstracted clown :)

On Thursday, 18 August 2022 at 14:00:15 UTC+2, richar...@gmail.com wrote:
> (And refusing to define what you means, means your statement is
> meaningless).
So your refusal to define "define", "means" and "meaningless" mustmean that the above sentence is meaningless, right?

> Yep, YOU are the discontinuity, and show you don't understand the math
> you are spouting.
**I** am not the discontinuity, you fucking retard.

Any ARBITRARILY CHOSEN LOCATION (colloquially refered to as the number 0) on the continuum is the discontinuity!

On Thursday, 18 August 2022 at 14:11:25 UTC+2, richar...@gmail.com wrote:
> And if you think Humans are computers you think too little of yourself.
The USE of the English word "I" exemplifies self-reference. Recursion!

I compute. But the "compute" is superfluous.

> Hard to make that point when Mathematics vastly predate Computers.
Mathematics predates the humans (who compute) ?!?!? Idiot.

> What Computer did Pythagoras use to make his proofs?
You think people before Pythagoras didn't compute?!?

You fucking idiot!

> I don't think you actually understand computer science either.
Oh, I think I understand recursion/self-reference just fine.

Skep Dick <skepdick22@gmail.com> wrote:
> On Thursday, 18 August 2022 at 13:45:43 UTC+2, Alan Mackenzie wrote:
>> You want a conversation? You may be as smart as me, whatever that
>> means, but you are not educated in mathematics to any degree; I am.
> Hahahahahaha! Translation in English.

> "I am smarter about Mathematics than you are"

> You fucking idiot.

You've lost the argument, so you descend to abuse. Where're your
"manners" now?

>> Manners, eh? To manners belongs respect.
> It's difficult to respect anyone who equates education with
> understanding.

With education comes understanding. You seem to be lacking in both.

>>If the subject of the thread were special purpose computer languages
> Special purpose computer languages is PRECISELY the subject of the
> thread!

> That is what Mathematics IS! A special-purpose language. Used by
> computers (a.k.a HUMANS).

> A "special purpose computer language" is also known as a FORMAL
> LANGUAGE.

>>I would respect your special knowledge on the topic, and wouldn't keep
>>pestering you with stupidities about the basics.

> "The basics" of Mathematics are computer science! You fucking idiot.

Hahahahahahaha! Yes I think you were right; I am smarter than you.

>> A number of people in this thread have expertise on mathematics that you
>> lack. Respect for that expertise is due from you. So far, you haven't
>> shown any.
> My expertise in computer science trumps your "expertise" in Mathematics.

> You fucking idiot.

>> Grow up.
> I am all grown up. But... to manners belong respect.

Curse words are incompatible with good manners.

> No respect from you - no manners from me.

--
Alan Mackenzie (Nuremberg, Germany).

On Thursday, 18 August 2022 at 14:21:00 UTC+2, Alan Mackenzie wrote:
> Skep Dick <skepd...@gmail.com> wrote:
> You've lost the argument, so you descend to abuse. Where're your
> "manners" now?
I already told you.

You'll get manners from me when I get respect from you.

> With education comes understanding. You seem to be lacking in both.
No, with understanding comes understanding.

Despite your edication, you don't seem to understand what it means to understand.

But let me not get too recursive on you - you seem to struggle with compter science.

> > "The basics" of Mathematics are computer science! You fucking idiot.
> Hahahahahahaha! Yes I think you were right; I am smarter than you.
Well, I always knew you believed that ;)

It's precisely because your over-abstracted ass needs to come back down to earth is why I keep calling you a "fucking idiot".

Consider it an attempt to ground your ego.

> Curse words are incompatible with good manners.
Which part of "My good manners are reserved for people with respect" went over your head?

You fucking idiot.