Students:

Can you tell me in one short sentence what is the definition of number?

Probably not.

Can your math teachers or professors tell you?

Definitely not.

Now ask yourself why this is so. Number is the first most important concept in mathematics. Euclid wrote 6 books before he tried to define number in Book 7.

He didn't quite make it, but a brilliant descendant of the Ancient Greeks called John Gabriel, succeeded!

A NUMBER is a NAME given to a MEASURE that describes a MAGNITUDE or SIZE.

Get a peak into the mind of a genius by studying my superbly written article on how I realised the concept of number:

https://drive.google.com/file/d/1hasWyQCZyRN3RkdvIB6bnGIVV2Rabz8w

My intellectual inferiors of the mainstream hate me for this. I am a persona non-grata in any moderated forum because I don't stand for bullshit. I tell it like it is.

The Trump supporters in mainstream math academia are those who will continue to keep you ignorant and lead you astray.

To understand mathematics, you need me. You CANNOT do it without me.

No one on the planet understands mathematics as profoundly as I do. I am a genius and yes, I do know better than anyone else.

Don't believe me? Hey, study my work! What do you have to lose? Chuckle.

Eram semper recta wrote:

> A NUMBER is a NAME given to a MEASURE that describes a MAGNITUDE or
> SIZE.

not true, the first natural numbers are integers, which are countable, a
1:many relationship. And actually you don't need numbers to describe
magnitudes and size, you just compare to some standard size or magnitude,
to make an overview, telling you is smaller or larger.

But remember, first numbers were integers, used counting objects. You get
everything wrong and upside down. Do NOT take the booster vaccine, it's
not a booster nor a vaccine!

On Wednesday, July 21, 2021 at 3:35:16 PM UTC-4, Eram semper recta wrote:
> Students:
>
> Can you tell me in one short sentence what is the definition of number?
>

For the purposes of informal discourse, just about any dictionary definition will do.

For the purposes of writing rigorous mathematical proofs, however, a good working definition of a natural number would be any element of the set N where N, S and 0 are such that:

1. 0 in N
2. S: N --> N
3. S is injective
4. For all x in N, S(x)=/=0
5. For all subsets P of N: [0 in P & For all x in P: [S(x) in P]

Starting from these axioms, most if not all of modern number theory can be derived using basic logic and set theory.

[snip]
>
> No one on the planet understands mathematics as profoundly as I do.

OMG...

WARNING TO STUDENTS: Don't become a victim of JG's fake math

JG here claims to have a discovered as shortcut to mastering calculus without using limits. Unfortunately for him, this means he has no workable a definition of the derivative of a function. It blows up for functions as simple f(x)=|x|. Or even f(x)=0. As a result, he has had to ban 0, negative numbers and instantaneous rates of change rendering his goofy little system quite useless. What a moron!

Forget calculus. JG has also banned all axioms because he cannot even derive the most elementary results of basic arithmetic, e.g. 2+2=4. Such results require the use of axioms, so he must figure he's now off the hook. Again, what a moron!

Even at his advanced age (60+?), John Gabriel is STILL struggling with basic, elementary-school arithmetic. As he has repeatedly posted here:

"There are no points on a line."
--April 12, 2021

"Pi is NOT a number of ANY kind!"
--July 10, 2020

"1/2 not equal to 2/4"
--October 22, 2017

“1/3 does NOT mean 1 divided by 3 and never has meant that”
-- February 8, 2015

"3 =< 4 is nonsense.”
--October 28, 2017

"Zero is not a number."
-- Dec. 2, 2019

"0 is not required at all in mathematics, just like negative numbers."
-- Jan. 4, 2017

“There is no such thing as an empty set.”
--Oct. 4, 2019

“3 <=> 2 + 1 or 3 <=> 8 - 5, etc, are all propositions” (actually all are meaningless gibberish)
--Oct. 22, 2019

No math genius our JG, though he actually lists his job title as “mathematician” at Linkedin.com. Apparently, they do not verify your credentials.

Though really quite disturbing, interested readers should see: “About the spamming troll John Gabriel in his own words...” (lasted updated March 10, 2020) at https://groups.google.com/forum/#!msg/sci.math/PcpAzX5pDeY/1PDiSlK_BwAJ

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog a http://www.dcproof.wordpress.com

On Wednesday, July 21, 2021 at 3:35:16 PM UTC-4, I am Super Rectum (aka John Gabriel, Troll Boy) wrote:
> Students:
>
> Can you tell me in one short sentence what is the definition of number?
>

For the purposes of informal discourse, just about any dictionary definition will do.

For the purposes of writing rigorous mathematical proofs, however, a good working definition of a natural number would be any element of the set N where N, S and 0 are such that:

1. 0 in N
2. S: N --> N
3. S is injective
4. For all x in N, S(x)=/=0
5. For all subsets P of N: [0 in P & For all x in P: [S(x) in P] => P=N]

Starting from these axioms, most if not all of modern number theory can be derived using basic logic and set theory.

[snip]
>
> No one on the planet understands mathematics as profoundly as I do.

OMG...

WARNING TO STUDENTS: Don't become a victim of JG's fake math

JG here claims to have a discovered as shortcut to mastering calculus without using limits. Unfortunately for him, this means he has no workable a definition of the derivative of a function. It blows up for functions as simple f(x)=|x|. Or even f(x)=0. As a result, he has had to ban 0, negative numbers and instantaneous rates of change rendering his goofy little system quite useless. What a moron!

Forget calculus. JG has also banned all axioms because he cannot even derive the most elementary results of basic arithmetic, e.g. 2+2=4. Such results require the use of axioms, so he must figure he's now off the hook. Again, what a moron!

Even at his advanced age (60+?), John Gabriel is STILL struggling with basic, elementary-school arithmetic. As he has repeatedly posted here:

"There are no points on a line."
--April 12, 2021

"Pi is NOT a number of ANY kind!"
--July 10, 2020

"1/2 not equal to 2/4"
--October 22, 2017

“1/3 does NOT mean 1 divided by 3 and never has meant that”
-- February 8, 2015

"3 =< 4 is nonsense.”
--October 28, 2017

"Zero is not a number."
-- Dec. 2, 2019

"0 is not required at all in mathematics, just like negative numbers."
-- Jan. 4, 2017

“There is no such thing as an empty set.”
--Oct. 4, 2019

“3 <=> 2 + 1 or 3 <=> 8 - 5, etc, are all propositions” (actually all are meaningless gibberish)
--Oct. 22, 2019

No math genius our JG, though he actually lists his job title as “mathematician” at Linkedin.com. Apparently, they do not verify your credentials.

Though really quite disturbing, interested readers should see: “About the spamming troll John Gabriel in his own words...” (lasted updated March 10, 2020) at https://groups.google.com/forum/#!msg/sci.math/PcpAzX5pDeY/1PDiSlK_BwAJ

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog a http://www.dcproof.wordpress.com

On Wednesday, 21 July 2021 at 15:44:35 UTC-4, Van Croft wrote:
> Eram semper recta wrote:
>
> > A NUMBER is a NAME given to a MEASURE that describes a MAGNITUDE or
> > SIZE.
> not true,

It is true, you imbecile!

> the first natural numbers are integers,

Bullshit! Both natural numbers and integers are ratios which means that A NUMBER is a NAME given to a MEASURE that describes a MAGNITUDE or SIZE.

<You are a very stupid person and I have no time to educate you. Read my article, you fucking moron!!!>

> which are countable, a
> 1:many relationship. And actually you don't need numbers to describe
> magnitudes and size, you just compare to some standard size or magnitude,
> to make an overview, telling you is smaller or larger.
>
> But remember, first numbers were integers, used counting objects. You get
> everything wrong and upside down. Do NOT take the booster vaccine, it's
> not a booster nor a vaccine!

Anonymous coward and king troll of sci.math Dan Christensen spammed:

> "There are no points on a line."

Lie. I never said that. What I did say is that a line does not consists of points. When we talk about points on a line, we really mean distances that are indicated much like road signs do for distances travelled along a road.

A line is one of innumerable distances between any two points.
A straight line is the shortest distance between two points.

> "Pi is NOT a number of ANY kind!"

True. Pi is merely a symbol for an incommensurable magnitude - apparently a concept too advanced for an imbecile like Dan Christensen.

> "1/2 not equal to 2/4"

Lie. I have NEVER said this. What I have talked about is the difference in the process of measure.
What does this mean? Well, 1/2 is the name given to a measure done by enumerating 1 of two equal parts of the unit.
2/4 is the name given to a measure done by enumerating 2 of four equal parts of the unit.

There is the case in geometry where 1/2 is not necessarily equal to 2/4. For example:

_ / _ _
_ _ / _ _ _ _

The length _ is not equal to the length _ _ .

> “1/3 does NOT mean 1 divided by 3 and never has meant that”

True. My brilliant article on how a genius mind discovers number and indeed how my brilliant ancestors (Ancient Greeks) realised number explains in detail:

https://drive.google.com/file/d/1hasWyQCZyRN3RkdvIB6bnGIVV2Rabz8w

Also, my article on pi not being a number of any kind:

https://drive.google.com/file/d/1FFg_9XCkIwTZ9N1jbU4oMYfHHHuFHYf3

The true story of how we got numbers:

https://drive.google.com/file/d/0B-mOEooW03iLYTg1TGY4RTIwakU

No such thing as a "real number" or a "real number line":

https://drive.google.com/file/d/0B-mOEooW03iLMHVYcE8xcmRZRnc

There is no valid construction of "real number" - it's a myth:

https://drive.google.com/file/d/0B-mOEooW03iLSTROakNyVXlQUEU

> "3 =< 4 is nonsense.”

True. In mathematics, it is called an invalid disjunction.

3 <= 4 means EITHER 3 < 4 OR 3 = 4

Actually, there is no "OR" part, so the logical disjunction is invalid.

> "Zero is not a number."

True. While not a number of any kind, it is very useful in mathematics.

https://drive.google.com/file/d/1w2tt7IgoIu-ychDCoYi-4jOAzToy0ViM

> "0 is not required at all in mathematics, just like negative numbers."

Half-truth. While negative numbers are not required in mathematics, they are extremely useful.

> “There is no such thing as an empty set.”

True. Even the father of all mainstream mathematical cranks rejected the idea of empty set. But let's not go too far ... there isn't even a definition of "set" in set theory!

https://youtu.be/KvxjOMW6Q9w

https://youtu.be/1CcSsOG0okg

> “3 <=> 2 + 1 or 3 <=> 8 - 5, etc, are all propositions” (actually all are meaningless gibberish)

True. These are propositions that are implied by the given equations. For example, my historic geometric identity states:

[f(x+h)-f(x)]/h = dy/dx + Q(x,h)

And so, f(x+h)-f(x)]/h <=> dy/dx + Q(x,h)

The theorem:

https://drive.google.com/file/d/1RDulODvgncItTe7qNI1d8KTN5bl0aTXj

How it provides a rigorous definition of integral for the flawed mainstream calculus:

https://drive.google.com/file/d/1uIBgJ1ObroIbkt0V2YFQEpPdd8l-xK6y

> Though really quite disturbing, interested readers should see:

The day will come when this vicious anonymous troll Dan Christensen is convicted in a court of law.

Download for free the most important mathematics book ever written:

https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view

On Wednesday, July 21, 2021 at 6:05:48 PM UTC-4, I am Super Rectum (aka John Gabriel, Troll Boy) wrote:

What Troll Boy snipped and couldn't refute:

[quote]

For the purposes of informal discourse, just about any dictionary definition will do.

For the purposes of writing rigorous mathematical proofs, however, a good working definition of a natural number would be any element of the set N where N, S and 0 are such that:

1. 0 in N
2. S: N --> N
3. S is injective
4. For all x in N, S(x)=/=0
5. For all subsets P of N: [0 in P & For all x in P: [S(x) in P] => P=N]

Starting from these axioms, most if not all of modern number theory can be derived using basic logic and set theory.

[unquote]

WARNING TO STUDENTS: Don't become a victim of JG's fake math

> > "1/2 not equal to 2/4"
> Lie. I have NEVER said this.

A direct quote from October 22, 2017 here at sci.math

> What I have talked about is the difference in the process of measure.
> What does this mean? Well, 1/2 is the name given to a measure done by enumerating 1 of two equal parts of the unit.
> 2/4 is the name given to a measure done by enumerating 2 of four equal parts of the unit.
>
> There is the case in geometry where 1/2 is not necessarily equal to 2/4. For example:
>

When will you learn, Troll Boy? 1/2 is ALWAYS EQUAL to 2/4.

[snip]

> > “1/3 does NOT mean 1 divided by 3 and never has meant that”
> True. My brilliant article on how a genius mind discovers number and indeed how my brilliant ancestors (Ancient Greeks) realised number explains in detail...

If you can't dazzle them brilliance, baffle them with bullshit, right, Troll Boy?

> > "3 =< 4 is nonsense.”
> True. In mathematics, it is called an invalid disjunction.
>

Nothing "invalid" about it, Troll Boy.

> 3 <= 4 means EITHER 3 < 4 OR 3 = 4
>

It means 3 < 4 OR 3 = 4, which is always truly.

See: https://en.wikipedia.org/wiki/Truth_table#Logical_disjunction_(OR)

[snip]

> > "Zero is not a number."
> True. While not a number of any kind, it is very useful in mathematics.
>

It really is a number, Troll Boy. Deal with it.

> > "0 is not required at all in mathematics, just like negative numbers."

> Half-truth.

Nope. Completely false.

> While negative numbers are not required in mathematics, they are extremely useful.

<yawn!>

> > “There is no such thing as an empty set.”

> True.

Umm... What about the set of all your brilliant mathematical discoveries? Empty.

[snip]

> > “3 <=> 2 + 1 or 3 <=> 8 - 5, etc, are all propositions”

> True.

Nope. The biconditional is logical connective. See https://en.wikipedia.org/wiki/Logical_biconditional

3 is not a logical proposition or a statement that is true or false. 3 is a number. So 3 <=> 2+1 would be an error in syntax. Deal with it, Troll Boy.

[snip]

> > Though really quite disturbing, interested readers should see: “About the spamming troll John Gabriel in his own words...” (lasted updated March 10, 2020) at

https://groups.google.com/forum/#!msg/sci.math/PcpAzX5pDeY/1PDiSlK_BwAJ

Also, all direct quotes from you, Troll Boy. To the extent that you will be remembered at all, history will not be kind to you. Time to cut your losses and move on Troll Boy.

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

Crank John Gabrial, aka Eram semper recta wrote:
> Students:

You have no student, John.

> No one on the planet understands mathematics as profoundly as I do. I am a genius and yes, I do know better than anyone else.

You're a delusional pathetic idiot.

> Don't believe me? Hey, study my work! What do you have to lose?

Time, even if studying your pathology is still a kind of study.

Anonymous coward and king troll of sci.math Dan Christensen spammed:

> "There are no points on a line."

Lie. I never said that. What I did say is that a line does not consists of points. When we talk about points on a line, we really mean distances that are indicated much like road signs do for distances travelled along a road.

A line is one of innumerable distances between any two points.
A straight line is the shortest distance between two points.

> "Pi is NOT a number of ANY kind!"

True. Pi is merely a symbol for an incommensurable magnitude - apparently a concept too advanced for an imbecile like Dan Christensen.

> "1/2 not equal to 2/4"

Lie. I have NEVER said this. What I have talked about is the difference in the process of measure.
What does this mean? Well, 1/2 is the name given to a measure done by enumerating 1 of two equal parts of the unit.
2/4 is the name given to a measure done by enumerating 2 of four equal parts of the unit.

There is the case in geometry where 1/2 is not necessarily equal to 2/4. For example:

_ / _ _
_ _ / _ _ _ _

The length _ is not equal to the length _ _ .

> “1/3 does NOT mean 1 divided by 3 and never has meant that”

True. My brilliant article on how a genius mind discovers number and indeed how my brilliant ancestors (Ancient Greeks) realised number explains in detail:

https://drive.google.com/file/d/1hasWyQCZyRN3RkdvIB6bnGIVV2Rabz8w

Also, my article on pi not being a number of any kind:

https://drive.google.com/file/d/1FFg_9XCkIwTZ9N1jbU4oMYfHHHuFHYf3

The true story of how we got numbers:

https://drive.google.com/file/d/0B-mOEooW03iLYTg1TGY4RTIwakU

No such thing as a "real number" or a "real number line":

https://drive.google.com/file/d/0B-mOEooW03iLMHVYcE8xcmRZRnc

There is no valid construction of "real number" - it's a myth:

https://drive.google.com/file/d/0B-mOEooW03iLSTROakNyVXlQUEU

> "3 =< 4 is nonsense.”

True. In mathematics, it is called an invalid disjunction.

3 <= 4 means EITHER 3 < 4 OR 3 = 4

Actually, there is no "OR" part, so the logical disjunction is invalid.

> "Zero is not a number."

True. While not a number of any kind, it is very useful in mathematics.

https://drive.google.com/file/d/1w2tt7IgoIu-ychDCoYi-4jOAzToy0ViM

> "0 is not required at all in mathematics, just like negative numbers."

Half-truth. While negative numbers are not required in mathematics, they are extremely useful.

> “There is no such thing as an empty set.”

True. Even the father of all mainstream mathematical cranks rejected the idea of empty set. But let's not go too far ... there isn't even a definition of "set" in set theory!

https://youtu.be/KvxjOMW6Q9w

https://youtu.be/1CcSsOG0okg

> “3 <=> 2 + 1 or 3 <=> 8 - 5, etc, are all propositions” (actually all are meaningless gibberish)

True. These are propositions that are implied by the given equations. For example, my historic geometric identity states:

[f(x+h)-f(x)]/h = dy/dx + Q(x,h)

And so, f(x+h)-f(x)]/h <=> dy/dx + Q(x,h)

The theorem:

https://drive.google.com/file/d/1RDulODvgncItTe7qNI1d8KTN5bl0aTXj

How it provides a rigorous definition of integral for the flawed mainstream calculus:

https://drive.google.com/file/d/1uIBgJ1ObroIbkt0V2YFQEpPdd8l-xK6y

> Though really quite disturbing, interested readers should see:

The day will come when this vicious anonymous troll Dan Christensen is convicted in a court of law.

Download for free the most important mathematics book ever written:

https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view

On Wednesday, 21 July 2021 at 21:27:51 UTC-4, Psychopath Jean Pierre Messager aka YBM aka JPM aka Python wrote:

> You have ..<shit>

Thanks for your two cents. Now perhaps you would be able to tell my students what is a number in one short sentence? LMAO.

On Thursday, July 22, 2021 at 7:46:52 AM UTC-4, I am Super Rectum (aka John Gabriel, Troll Boy) wrote:

> Thanks for your two cents. Now perhaps you would be able to tell my students what is a number in one short sentence? LMAO.

What "students," Troll Boy? Anyway, IF you DID have a student, you might consider:

A natural number is any element of a set N in which there exists a "first number" denoted by '0', and for every element of N there exists a unique "next number" in N, different numbers having a different "next number," and every element of N but 0 can be reached, starting at 0 and repeatedly going to the next number in succession.

This has been basic common number sense for thousands of years. (Although, the "first number" has often been denoted by '1'.)

Note, this definition is formalized by Peano's Axioms. In the language of set theory:

1. 0 in N
2. For all x in N: [S(x) in N
3. For all x, y in N: [S(x)=S(y) => x=y]
4. For all x in N: [S(x)=/=0
5 For all subsets P of N: [0 in P & For all x in P: [S(x) in P] => P=N]

Starting from these axioms, most if not all of modern number theory can be derived using only basic logic and set theory.

What can you derive from your, ahem... "definition" of a number, Troll Boy? How about 2+2=4? No, not yet??? Oh, well...

Dan

Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com

On Wednesday, 21 July 2021 at 15:35:16 UTC-4, Eram semper recta wrote:
> Students:
>
> Can you tell me in one short sentence what is the definition of number?
>
> Probably not.
>
> Can your math teachers or professors tell you?
>
> Definitely not.
>
> Now ask yourself why this is so. Number is the first most important concept in mathematics. Euclid wrote 6 books before he tried to define number in Book 7.
>
> He didn't quite make it, but a brilliant descendant of the Ancient Greeks called John Gabriel, succeeded!
>
> A NUMBER is a NAME given to a MEASURE that describes a MAGNITUDE or SIZE.
>
> Get a peak into the mind of a genius by studying my superbly written article on how I realised the concept of number:
>
> https://drive.google.com/file/d/1hasWyQCZyRN3RkdvIB6bnGIVV2Rabz8w
>
> My intellectual inferiors of the mainstream hate me for this. I am a persona non-grata in any moderated forum because I don't stand for bullshit. I tell it like it is.
>
> The Trump supporters in mainstream math academia are those who will continue to keep you ignorant and lead you astray.
>
> To understand mathematics, you need me. You CANNOT do it without me.
>
> No one on the planet understands mathematics as profoundly as I do. I am a genius and yes, I do know better than anyone else.
>
> Don't believe me? Hey, study my work! What do you have to lose? Chuckle.

My dear students:

With every comment I make, I demonstrate yet again the problems with mainstream mathematics, the way it is taught and the toxic groupthink that has become a cult.

My fight has cost me two teaching jobs at private schools even before I got to teach a single lesson. I will never be hired again due to the libel by trolls on this (in particular the anonymous scumbag Dan Christensen) and other newsgroups and forums. So I teach independently only. It has also made me homeless, but has not destroyed my spirit.

Aside from being a genius, I am actually an incredible human being. The way I have been persecuted by all these vile bastards is practically a sin.

The more I publish truth, the more I am hated for it.

My opponents are seething with anger and jealousy and will go to any lengths to obstruct my great work and destroy me personally if possible. About 4.5 years ago, the scum on this forum under the leadership of Prof. Gilbert Strang of MIT tried to effect a contract murder on me whilst in South Africa.. One of the protagonists (scumbag Freda Parkins) crawled out of her sewer just recently thinking she could score a major win against me. This deluded bitch tried to justify her actions by claiming that an anon coward QB was being threatened. All the same, she did not harm me because as always, people like her don't actually see what is, only what they want to see.

Now sci.math is an unmoderated newsgroup and the ONLY one where I can advertise my great work. I shall continue to ruthlessly expose the mainstream in every possible respect. I hate them.

Eram semper recta wrote:

> On Wednesday, 21 July 2021 at 15:44:35 UTC-4, Van Croft wrote:
>> Eram semper recta wrote:
>>
>> > A NUMBER is a NAME given to a MEASURE that describes a MAGNITUDE or
>> > SIZE.
>> not true,
>
> It is true, you imbecile!

Why are you then split shit into small pieces, you uneducated cretin with
a mouth?

>> the first natural numbers are integers,
>
> Bullshit! Both natural numbers and integers are ratios which means that
> A NUMBER is a NAME given to a MEASURE that describes a MAGNITUDE or
> SIZE.

Can't you read the argument, you stupid rectal? The first observation
after birth are the fingers, which are countable integers. That takes
precedence. Then magnitudes and sizes were determined *_without_* numbers
for thousands of years, you uneducated inbreed idiot.

On Thursday, July 22, 2021 at 10:01:26 AM UTC-4, I am Super Rectum (aka John Gabriel) wrote:

> My opponents are seething with anger and jealousy and will go to any lengths to obstruct my great work...

On the contrary, I'm just encouraging your to fill in some HUGE GAPS in your, ahem... "great work," e.g. proving 2+2=4, determining the derivative of f(x)=|x|. Think of it as constructive criticism. ;^)

Dan

Eram semper recta wrote:
> Students:
>
> Can you tell me in one short sentence what is the definition of number?
>
> Probably not.

I agree. The definition of natural number as finite von Neumann ordinal
(say, there are other possibilities) will take more than one sentence,
short or otherwise. And then there are the integers, rational numbers,
real numbers, complex numbers,... Just what sort of number are you
asking about?

--
The world will little note, nor long remember what we say here
Abraham Lincoln at Gettysburg

Eram semper recta wrote:

>> "There are no points on a line."
>
> Yvr. V arire fnvq gung. Jung V qvq fnl vf gung n yvar qbrf abg pbafvfgf
> bs cbvagf. Jura jr gnyx nobhg cbvagf ba n yvar, jr ernyyl zrna qvfgnaprf
> gung ner vaqvpngrq zhpu yvxr ebnq fvtaf qb sbe qvfgnaprf geniryyrq nybat
> n ebnq.
>
> N yvar vf bar bs vaahzrenoyr qvfgnaprf orgjrra nal gjb cbvagf.
> N fgenvtug yvar vf gur fubegrfg qvfgnapr orgjrra gjb cbvagf.

nothing. You over there are all immigrants. Toilet paper shortage, makes
me depressed.

On Thursday, 22 July 2021 at 11:42:26 UTC-4, Peter wrote:
> Eram semper recta wrote:
> > Students:
> >
> > Can you tell me in one short sentence what is the definition of number?
> >
> > Probably not.

> I agree.

Wrong! There is a definition in one short sentence:

A number is a NAME given to a MEASURE that describes a MAGNITUDE or SIZE.

> The definition of natural number as finite von Neumann ordinal

Oh, please!!! von Neumann was an idiot deluxe!! Don't tell me this please. Think, idiot! Think!

> (say, there are other possibilities) will take more than one sentence,
> short or otherwise. And then there are the integers, rational numbers,
> real numbers, complex numbers,... Just what sort of number are you
> asking about?

There is ONLY one kind of NUMBER and it is called a RATIONAL NUMBER. There are NO other numbers. Chuckle.

>

Eram semper recta wrote:

>> "Pi is NOT a number of ANY kind!"
>
> True. Pi is merely a symbol for an incommensurable magnitude -
> apparently a concept too advanced for an imbecile like Dan Christensen.

Substitute "incommensurable magnitude" (not magnitude) with
*transcendental*. It's a number, not symbol. You use a symbol to express
that transcendental number. Kindergarten stuff in my country.

Don't believe me, read this and pay attention

SHOCKING VIDEO OF FORCED VAXTERMINATIONS
https://www.bitchute.com/video/PnzY7lCX2Xhq/

The hidden truth they don't want you to know, the extermination WW2 was
through *lethal_injections*, not gas chambers. Effective, faster. The
history repeats itself.

On Thursday, July 22, 2021 at 12:50:40 PM UTC-4, I am Super Rectum (aka wrote:

>
> A number is a NAME given to a MEASURE that describes a MAGNITUDE or SIZE.

Completely useless for rigorously proving anything about numbers, e.g. not even 2+2=4. Back to the drawing board, though that would probably be waste of time in your case, Troll Boy. Better to scrap the whole project, cut your losses and get on with your life.

Dan

Hugh Jass wrote:

>>> "Pi is NOT a number of ANY kind!"
>>
>> True. Pi is merely a symbol for an incommensurable magnitude -
>> apparently a concept too advanced for an imbecile like Dan Christensen.
>
> Substitute "incommensurable magnitude" (not magnitude) with
> *transcendental*. It's a number, not symbol. You use a symbol to express
> that transcendental number. Kindergarten stuff in my country.
>
> Don't believe me, read this and pay attention
>
> SHOCKING VIDEO OF FORCED VAXTERMINATIONS
> https://www.bitchute.com/video/PnzY7lCX2Xhq/
>
> The hidden truth they don't want you to know, the extermination WW2 was
> through *lethal_injections*, not gas chambers. Effective, faster. The
> history repeats itself.

I am trying to save lives here. I may not succeed.

On Thursday, 22 July 2021 at 13:35:31 UTC-4, Hugh Jass wrote:
> Hugh Jass wrote:
>
> >>> "Pi is NOT a number of ANY kind!"
> >>
> >> True. Pi is merely a symbol for an incommensurable magnitude -
> >> apparently a concept too advanced for an imbecile like Dan Christensen.
> >
> > Substitute "incommensurable magnitude" (not magnitude) with
> > *transcendental*. It's a number, not symbol. You use a symbol to express
> > that transcendental number. Kindergarten stuff in my country.
> >
> > Don't believe me, read this and pay attention
> >
> > SHOCKING VIDEO OF FORCED VAXTERMINATIONS
> > https://www.bitchute.com/video/PnzY7lCX2Xhq/
> >
> > The hidden truth they don't want you to know, the extermination WW2 was
> > through *lethal_injections*, not gas chambers. Effective, faster. The
> > history repeats itself.
> I am trying to save lives here. I may not succeed.

SHUT UP YOU MORON!

Go and get vaccinated! It might help with your brain too!!!!

On Thursday, July 22, 2021 at 1:35:31 PM UTC-4, Hugh Jass wrote:
> Hugh Jass wrote:
>
> >>> "Pi is NOT a number of ANY kind!"
> >>
> >> True. Pi is merely a symbol for an incommensurable magnitude -
> >> apparently a concept too advanced for an imbecile like Dan Christensen.
> >
> > Substitute "incommensurable magnitude" (not magnitude) with
> > *transcendental*. It's a number, not symbol. You use a symbol to express
> > that transcendental number. Kindergarten stuff in my country.
> >
> > Don't believe me, read this and pay attention
> >
> > SHOCKING VIDEO OF FORCED VAXTERMINATIONS
> > https://www.bitchute.com/video/PnzY7lCX2Xhq/
> >
> > The hidden truth they don't want you to know, the extermination WW2 was
> > through *lethal_injections*, not gas chambers. Effective, faster. The
> > history repeats itself.

> I am trying to save lives here. I may not succeed.

Bullshit. You want to create chaos and even more social division.

Dan

On Thursday, 22 July 2021 at 14:39:03 UTC-4, Dan Christensen wrote:
> On Thursday, July 22, 2021 at 1:35:31 PM UTC-4, Hugh Jass wrote:
> > Hugh Jass wrote:
> >
> > >>> "Pi is NOT a number of ANY kind!"
> > >>
> > >> True. Pi is merely a symbol for an incommensurable magnitude -
> > >> apparently a concept too advanced for an imbecile like Dan Christensen.
> > >
> > > Substitute "incommensurable magnitude" (not magnitude) with
> > > *transcendental*. It's a number, not symbol. You use a symbol to express
> > > that transcendental number. Kindergarten stuff in my country.
> > >
> > > Don't believe me, read this and pay attention
> > >
> > > SHOCKING VIDEO OF FORCED VAXTERMINATIONS
> > > https://www.bitchute.com/video/PnzY7lCX2Xhq/
> > >
> > > The hidden truth they don't want you to know, the extermination WW2 was
> > > through *lethal_injections*, not gas chambers. Effective, faster. The
> > > history repeats itself.
>
> > I am trying to save lives here. I may not succeed.
> Bullshit. You want to create chaos and even more social division.

He is very much like YOU, only more so! LMAO.

>
> Dan

On Wednesday, July 21, 2021 at 12:35:16 PM UTC-7, Eram semper recta wrote:
> Students:
>
> Can you tell me in one short sentence what is the definition of number?
>

You should not need them to understand math you moron Gabriel...

Mitchell Raemsch

On Thursday, July 22, 2021 at 10:35:31 AM UTC-7, Hugh Jass wrote:
> Hugh Jass wrote:
>
> >>> "Pi is NOT a number of ANY kind!"
> >>
> >> True. Pi is merely a symbol for an incommensurable magnitude -
> >> apparently a concept too advanced for an imbecile like Dan Christensen.
> >
> > Substitute "incommensurable magnitude" (not magnitude) with
> > *transcendental*. It's a number, not symbol. You use a symbol to express
> > that transcendental number. Kindergarten stuff in my country.
> >
> > Don't believe me, read this and pay attention
> >
> > SHOCKING VIDEO OF FORCED VAXTERMINATIONS
> > https://www.bitchute.com/video/PnzY7lCX2Xhq/
> >
> > The hidden truth they don't want you to know, the extermination WW2 was
> > through *lethal_injections*, not gas chambers. Effective, faster. The
> > history repeats itself.
> I am trying to save lives here. I may not succeed.

How is your ass going to do it?