Georg Cantor was a mentally disturbed self-confessed Jew who was born in Russia and died in Germany.

His claim to fame is the observation that certain sets can be systematically named or listed. This observation became the basis for his bullshit theory of bijective cardinality.

There are several ways to define a countable set A:

i. A is countable if and only if, its members can be systematically named..
ii. A is countable, if and only if, its members can be systematically indexed.
iii. A is countable, if and only if, its members can be systematically listed.

In order to index a given set with another set (such as the natural numbers or rational numbers), it must be the case that the index set is itself countable, that is, its members can be systematically named. This is indeed the case where the natural numbers and rational numbers are concerned. For example, the natural numbers can be systematically named using any positional radix system such as base 10 or decimal. As for the rational numbers, there is the Cantor pairing function.

Cantor’s ideas were initially just laughed at for what they were – nonsense. However, his followers (such as the retarded David Hilbert and others) exerted much effort in promoting Cantor’s rotten ideas to the point of toxicity. Unfortunately, Cantor’s garbage found its way into mainstream mathematics and set back its study several hundred years. I would be a millionaire if I had a dollar for every clown who calls himself or herself a set theorist or topologist.

His unremarkable initial idea of countable set would have been benign had Cantor’s drivel ceased then. However, the absolute rot of his theories progressed to different levels of infinity (when even infinity itself is a 100% junk concept) and to a wonderland where aleph numbers reign supreme.. Bijective cardinality is the idea that given any two infinite sets, the elements can be mapped from one set to another. The first problem with this idea is that points have no size, dimension or extent, so the only way to think about the problem is to interpret the distinct elements as distances, in which case there is nothing remarkable because the problem is one of scaling one distance to another. This elementary knowledge was known to cartographers long before Cantor was born.

Since crank Cantor could not name the elements of certain sets, he concluded the size of such sets could be assigned a cardinal number. ℵ0 was the symbol he introduced to denote the cardinality of the most basic countable set, that of the natural numbers ℕ. It didn’t matter to Cantor that ℵ0 is not a number of any kind and cardinality implies number. “God had revealed these things to him over a period of twenty years” (sic). Given that these ideas were divinely inspired, Cantor and his crank followers had no qualms about injecting his hokum into mainstream mathematics courses. Even though no mainstream mathematics professor has a clue what is the concept of number or how to define it, students of mathematics are usually presented with the bowel movement known as the Diagonal Argument, which fails at the first step because one must accept that every mythical “real number” has an infinite decimal expansion, which is provable wrong and not just because infinity is an ill-formed concept that has no place in mathematics or any other field of rational thought.

One of Cantor’s delusions is that ∞ + ∞=∞.. In words, if one “infinite set” is added to another, the resulting set is infinite. This becomes problematic if the difference ∞ - ∞ is considered. Therefore, it is expressly forbidden by a formal decree issued by my intellectual inferiors of mainstream mathematics academia. There are so many problems with Cantor’s nonsensical theories and I don’t intend to address all of them here, save the blunder that the difference ∞ - ∞ is “undefined”.

Proof that ∞ - ∞ = 0 in contradiction to Cantor’s claims:

(1-x^(n+1))/(1-x)=1/(1-x)-(x^n+1)/(1-x)
=1+x+x^2+x^3+ …+x^n+[x^n+1+x^n+2+…]-[x^n+1+x^n+2+…] [ID]

where
(x^n+1)/(1-x)=-[x^n+1+x^n+2+…]
and
(1-x^n+1)/(1-x)=1+x+x^2+x^3+ … + x^n-1+x^n

because

1/(1-x)=1+x+x^2+x^3+ … + x^n-1+x^n+[x^n+1+x^n+2+…]

Now the sets [x^n+1, x^n+2 ,…] and -[x^n+1, x^n+2 ,…] possess the same cardinality given that they are described by exactly the same elements and it’s clear the only difference is in sign, that is, the elements of -[x^n+1, x^n+2 ,…] are all negative.

Therefore in order for [ID] to remain true, it must be the case that [x^n+1+x^n+2+…]+[x^n+1+x^n+2+…] = 0, that is,
∞ - ∞=0 must be true also which is in contradiction to Cantor’s decree! What else did you expect?

I am John Gabriel, the discoverer of the New Calculus, the first rigorous formulation of calculus in human history. Download my free eBook:

https://www.academia.edu/41616655/An_Introduction_to_the_Single_Variable_New_Calculus

Become a subscriber to my channel, the best math channel on the web:

https://www.youtube.com/channel/UClBbBVLs3M-d3dNgU4Vop_A/videos

On Saturday, 14 May 2022 at 09:13:10 UTC+3, Eram semper recta wrote:
> Georg Cantor was a mentally disturbed self-confessed Jew who was born in Russia and died in Germany.
>
> His claim to fame is the observation that certain sets can be systematically named or listed. This observation became the basis for his bullshit theory of bijective cardinality.
>
> There are several ways to define a countable set A:
>
> i. A is countable if and only if, its members can be systematically named..
> ii. A is countable, if and only if, its members can be systematically indexed.
> iii. A is countable, if and only if, its members can be systematically listed.
>
> In order to index a given set with another set (such as the natural numbers or rational numbers), it must be the case that the index set is itself countable, that is, its members can be systematically named. This is indeed the case where the natural numbers and rational numbers are concerned. For example, the natural numbers can be systematically named using any positional radix system such as base 10 or decimal. As for the rational numbers, there is the Cantor pairing function.
>
> Cantor’s ideas were initially just laughed at for what they were – nonsense. However, his followers (such as the retarded David Hilbert and others) exerted much effort in promoting Cantor’s rotten ideas to the point of toxicity. Unfortunately, Cantor’s garbage found its way into mainstream mathematics and set back its study several hundred years. I would be a millionaire if I had a dollar for every clown who calls himself or herself a set theorist or topologist.
>
> His unremarkable initial idea of countable set would have been benign had Cantor’s drivel ceased then. However, the absolute rot of his theories progressed to different levels of infinity (when even infinity itself is a 100% junk concept) and to a wonderland where aleph numbers reign supreme. Bijective cardinality is the idea that given any two infinite sets, the elements can be mapped from one set to another. The first problem with this idea is that points have no size, dimension or extent, so the only way to think about the problem is to interpret the distinct elements as distances, in which case there is nothing remarkable because the problem is one of scaling one distance to another. This elementary knowledge was known to cartographers long before Cantor was born.
>
> Since crank Cantor could not name the elements of certain sets, he concluded the size of such sets could be assigned a cardinal number. ℵ0 was the symbol he introduced to denote the cardinality of the most basic countable set, that of the natural numbers ℕ. It didn’t matter to Cantor that ℵ0 is not a number of any kind and cardinality implies number. “God had revealed these things to him over a period of twenty years” (sic). Given that these ideas were divinely inspired, Cantor and his crank followers had no qualms about injecting his hokum into mainstream mathematics courses. Even though no mainstream mathematics professor has a clue what is the concept of number or how to define it, students of mathematics are usually presented with the bowel movement known as the Diagonal Argument, which fails at the first step because one must accept that every mythical “real number” has an infinite decimal expansion, which is provable wrong and not just because infinity is an ill-formed concept that has no place in mathematics or any other field of rational thought.
>
> One of Cantor’s delusions is that ∞ + ∞=∞. In words, if one “infinite set” is added to another, the resulting set is infinite. This becomes problematic if the difference ∞ - ∞ is considered. Therefore, it is expressly forbidden by a formal decree issued by my intellectual inferiors of mainstream mathematics academia. There are so many problems with Cantor’s nonsensical theories and I don’t intend to address all of them here, save the blunder that the difference ∞ - ∞ is “undefined”.
>
> Proof that ∞ - ∞ = 0 in contradiction to Cantor’s claims:
>
> (1-x^(n+1))/(1-x)=1/(1-x)-(x^n+1)/(1-x)
> =1+x+x^2+x^3+ …+x^n+[x^n+1+x^n+2+…]-[x^n+1+x^n+2+…] [ID]
>
> where
> (x^n+1)/(1-x)=-[x^n+1+x^n+2+…]
> and
> (1-x^n+1)/(1-x)=1+x+x^2+x^3+ … + x^n-1+x^n
>
> because
>
> 1/(1-x)=1+x+x^2+x^3+ … + x^n-1+x^n+[x^n+1+x^n+2+…]
>
> Now the sets [x^n+1, x^n+2 ,…] and -[x^n+1, x^n+2 ,…] possess the same cardinality given that they are described by exactly the same elements and it’s clear the only difference is in sign, that is, the elements of -[x^n+1, x^n+2 ,…] are all negative.
>
> Therefore in order for [ID] to remain true, it must be the case that [x^n+1+x^n+2+…]+[x^n+1+x^n+2+…] = 0, that is,
> ∞ - ∞=0 must be true also which is in contradiction to Cantor’s decree! What else did you expect?
>
> I am John Gabriel, the discoverer of the New Calculus, the first rigorous formulation of calculus in human history. Download my free eBook:
>
> https://www.academia.edu/41616655/An_Introduction_to_the_Single_Variable_New_Calculus
>
> Become a subscriber to my channel, the best math channel on the web:
>
> https://www.youtube.com/channel/UClBbBVLs3M-d3dNgU4Vop_A/videos

The deluded moron followers of Cantor reasoned that subtracting infinity from another infinity is the same as removing part of an infinite set, in other words, the result can be infinite if the set removed is smaller [the fucking idiots of mainstream mythmatics will say that (0,1) is greater than (0,1/2), but (0,1)-(0,1/2) is indeterminate which is obviously garbage since what is left is (1/2,1)] or 0 if the whole set is removed. The feeble excuse of my intellectual inferiors in the mainstream is that it can't be both 0 and ∞ which is true. Therefore the syphilitic brains decrees such an operation is "indeterminate".

To say ∞ + ∞ = ∞ does not affect their peanut brains, but there is a disconnect with ∞ - ∞=0 because "infinities" have different sizes! Chuckle. However, if "infinities" have the same size, that is, (2,3)-(2,3), then the result is 0. Experiencing a good eye-roll now...

It's no wonder that mathematics students drop out of math courses when presented with this utter shit, because there really is no other way to describe Cantor's delusional theories.

You can detect a syphilitic brain from light years away - it's one which believes that ∞ is a well-formed concept.