The Wikipedia Moronica has this to say:
Cantor's theory of transfinite numbers was originally regarded as so counter-intuitive – even shocking – that it encountered resistance from mathematical contemporaries such as Leopold Kronecker and Henri Poincaré and later from Hermann Weyl and L. E. J. Brouwer, while Ludwig Wittgenstein raised philosophical objections.
Kronecker and Poincaré were both respectable mathematicians of their time. Well, I don't know if they were mathematicians for certain, because in my opinion, possessing a PhD in mathematics does not entitle one to be called a mathematician. Anyway, this is what they had to say:
Poincaré: Cantor's ideas are a "grave disease" infecting the discipline of mathematics.
Kronecker(Jewish): Cantor is a "scientific charlatan", a "renegade" and a "corrupter of youth."
Wittgenstein (philosophy PhD and most qualified to judge Cantor's anti-mathematical rot): ... lamented that mathematics is "ridden through and through with the pernicious idioms of set theory," which he dismissed as "utter nonsense" that is "laughable" and "wrong".
Mathematicians such as Brouwer and especially Poincaré adopted an intuitionist stance against Cantor's work. Citing the paradoxes of set theory as an example of its fundamentally flawed nature, Poincaré held that "most of the ideas of Cantorian set theory should be banished from mathematics once and for all."
Poincaré was correct. It's too bad that idiots the likes of Hilbert decided to do exactly the opposite.
What I would really like to do now, is not remove the morons from Cantor's delusional paradise, I would like to shove them all in as far as one can, lock the gate, and throw the key away! Let them stay in their delusions.
But for the sake of future generations, we need to deCantorize mathematics. Cantor's delusional ideas are the MIV (Mathematics immunity virus).
If I had a dollar for each worthless dissertation on number and set theory today, I would be a multi-millionaire.
While finite sets are useful, these ideas did not originate with Cantor. I am so weary of anything Cantor, that I would want to erase his name and memory entirely from mathematics where it never belonged.
I don't have anything personal against Cantor's memory, but I absolutely loathe what his ideas have done to mathematics. Rot in its purest form are the theories of Cantor.
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"Indeed [the limit is unlimited]"
"1 = 0.999... is the limit of the sequence 0.9, 0.99, 0.999, ..."
All the pieces are the same size. No piece has 0 area, and you can't cut the paper into infinitely many pieces even mathematically. The limit of the number of cuts you can make is oo. The limit of the smallest area is 0. No matter how small the pieces are, you can cut them in half again. -Chris Crank mental midget
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clearly an alias to troll under. "The obvious troll is obvious"
"Indeed [the limit is unlimited]"
"1 = 0.999... is the limit of the sequence 0.9, 0.99, 0.999, ..."
All the pieces are the same size. No piece has 0 area, and you can't cut the paper into infinitely many pieces even mathematically. The limit of the number of cuts you can make is oo. The limit of the smallest area is 0. No matter how small the pieces are, you can cut them in half again. -Chris Crank mental midget
Let's take a few steps back and think about this entire debate. In my mind there was never any doubt the equality is false, but being open minded as I am, I always left a tiny escape hatchet. After all, I did not wish to find myself among that group who had the wool pulled over their eyes.
Since 2000, I have debated the topic on some very large forums. You will find a major Wikipedia Moronica debate in its archives (I was participating as an Anon then because I had not made up my mind) between a user called Rasmus (Norwegian I think?) and me.
That debate revolved around complex mathematics that included inequalities, real numbers and the Archimedean property. I tired of the debate in the end, after I had repeatedly refuted their wrong assertions and left, leaving them to their ignorance. What I learned from that debate was that Wikipedia is run by their math gods (Arthur Rubin and Michael Hardy - both math PhDs). Bias in knowledge is very real.
I decided not to participate in a debate on this topic again, until I had irrefutable proof. Although my arguments in the Moronica debate were sound, they were not mathematical "enough" for the academic bourgeoisie. I spent more time developing the New Calculus because I was convinced that Newton, Leibniz and Cauchy are wrong. I told myself that if I could formulate calculus without limits, infinitesimals or any other ill-formed concepts, I would accomplish what no one else could in the history of man. So my efforts were focused on undoing the damage of the past 300 years. Impossible is not a word in my vocabulary. But the expressions well-defined and well-formed are at the core of my ideas.
Knowledge must essentially be so simple that even an idiot can understand it. My first encounter with calculus convinced me that it was flawed.
But before I stray too much off the topic, I decided to debate it one last time here on STATU. One should ask oneself why it is that this topic still rages on. It is far from settled or established knowledge. In this debate I have produced overwhelming evidence that the idea is wrong. I have shown beyond doubt that the Eulerian blunder is the original source of this fallacy. To be sure, quite a few ignorant mathematicians helped lead Euler to this flawed definition and incoherent way of thinking.
This thread is a model for those wanting to debunk all the purported "proofs" surrounding the fallacy that 0.999... and 1 are the same. But there is much, much more knowledge in this thread that can dispel many of the wrong concepts you were taught by your ignorant and incompetent "educators".
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In this comment I lay to rest Cantor's diagonal argument for good.
In my debate with Mark Chu Carroll, I was banned before I could even get this far.
There is not a single proof that the Diagonal Argument is in fact true. Nowhere on the internet or anywhere else.
The argument originally states that the set of "real" numbers in the interval (0,1) could not be listed. There was no mention of a one-to-one correspondence (bijection).
This statement is very quickly dismissed in the following diagram which lists (represents) every single one of the numbers in the interval (0,1):
diagonal.jpg
But mainstream baboons did not stop here. They reinterpreted Cantor's rot in the context of a one to one correspondence between the "real" numbers in the interval (0,1) and the natural numbers, that is, an enumeration.
I shall demonstrate now that we can place these "real" numbers in a one-to-one correspondence with a unique sequence which we'll call the index.
Every index sequence will be preceded by either +, - or *.
For example,
The number 0.3 has an index sequence of +3
0.03 has an index sequence of +03
0.(3) has an index sequence of -3
0.0(3) has an index sequence of -03
0.(15) has an index sequence of -15
0.26 has an index sequence of +26
0.14159... has an index sequence of *14159... (fractional part of pi)
0.391 has an index sequence of +391
As you can see, every index sequence is unique. What I have done is placed the "real" numbers in the interval (0,1) in correspondence with a unique index sequence, that is, I have created a bijection! In this scheme I have ENUMERATED the numbers in the interval (0,1). The decimal tree represents the numbers and the unique sequence index enumerates the same.
Now, if a bijection exists, then by mainstream theory, the interval must be countable, which is contrary to Cantor's claims.
So, provided one accepts that all the numbers in the interval (0,1) can be represented as decimals, then the "real" numbers are indeed countable.
This is the simplest proof that Cantor was a delusional idiot.
Disclaimer: I do not agree the "real" numbers are countable because one can't count a set containing non-existent objects. My tree in fact, only contains rational numbers, but moron academics think it contains all the "real" numbers in the interval (0,1).
Webster's entry for enumerate is:
enu·mer·ate transitive verb \i-ˈn(y)ü-mə-ˌrāt\
: to name (things) one after another in a list
I include this Webster definition here, in case any of you morons object to the use of +, - or * in my unique sequence index.
Last edited by john_gabriel; 01-29-2014 at 02:06 PM.
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Trust you to get it wrong again. Reading without your spectacles again? Yeah, I know. It happens to me a lot. I purposely remove them when I read your comments - that way, they make more sense. If you know what I mean...
Ask Mark Chu Carroll - he is a computer "scientist". I am surprised you don't think it contains "real" numbers. Carroll thinks it contains every "real" number. His beef is that it does not enumerate them. Well, now YOU know how they can be enumerated.
Is there any "real" number you think is missing? As far as I know, they are "all there"! Pick one, locate the first decimal digit, and traverse the tree away!!!
And what's more, a bijection exists. You pick a unique "real" number and I give you a unique sequence. You pick a unique sequence and I give you the unique "real" number. Isn't that just cool?
Last edited by john_gabriel; 01-27-2014 at 09:06 PM.
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This comment is to preempt false retorts by Grapes, etc, regarding a bijection.
From your very own Wikipedia Moronica:
(http://en.wikipedia.org/wiki/Countable_set)
Although a "bijection" seems a more advanced concept than a number, the usual development of mathematics in terms of set theory defines functions before numbers, as they are based on much simpler sets. This is where the concept of a bijection comes in: define the correspondence
a ↔ 1, b ↔ 2, c ↔ 3
Since every element of {a, b, c} is paired with precisely one element of {1, 2, 3}, and vice versa, this defines a bijection.
Note that this pairing of elements is an ENUMERATION.
The only part of my unique sequence index that is not a digit, is the first character which distinguishes between a finite radix representation (PLUS), a recurring decimal (MINUS) and an "irrational" number (ASTERISK).
So, it's clearly a bijection. Cantor's claim that the "real" numbers cannot be placed into a bijection with another set whose cardinality is infinity, is clearly false.
Disclaimer: "Real" numbers do not exist because "irrational" numbers do not exist. Cantor was actually correct that they are uncountable, but not because of his fake Diagonal Argument or any other reason, except the glaringly obvious, that is, "real" numbers don't exist!!! Poor, delusional Cantor!
After-thoughts: The idiot Mark Chu Carroll constantly harped on the fact that representation is not enumeration, after I had used Socratic arguments to have him admit my tree contains every real number (hard to deny when one believes that 0.333...=1/3 and 3.14159... = pi!).
He did not realise that agreeing to this, would place him directly on the losing end of the argument. You see, representation, although not quite the same as enumeration, is nine tenths of enumeration! You can't have enumeration without representation. Makes perfect sense, because if you can't represent an "irrational" number, then how do you expect to enumerate the number?!! Moron!
This is something I tried to teach Grapes and Colin. The fact that you can write pi= 3.14159... does not constitute a representation of pi at all! In truth, my tree only contains rational numbers, because 3.14159... is ALWAYS a rational number!! All the numbers in my tree are in fact RATIONAL NUMBERS. See, a non-terminating, non-repeating representation is a symptom of an incommensurable magnitude; it is NOT an "irrational" number. In the same way, a non-terminating, repeating representation (e.g. 0.333...) is a symptom of a rational number, it is NOT the rational number. The aforementioned, are properties of commensurable and incommensurable magnitudes in radix systems. Grapes should write this sentence down and hang it on his wall. He should read it every morning until he finally gets to understand what it means.
For those of you reading this comment without having read the entire thread, a proof that real numbers DO NOT EXIST can be found on page 317 of this thread.
Last edited by john_gabriel; 01-28-2014 at 04:08 AM.
The more I publish the truth, the more society hates me.
There is no sympathy for those who expose deeply flawed mainstream ideas.
The official New Calculus site
The 9 applet New Calculus course
Die Neue Analysis
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