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Posts tagged with "math"

Cantor's Theory Visualized

Cantor's theory is one of the most misunderstood theories of all times. It's what happens when one does not understand what they are doing. By that, I mean that Cantor thought he was comparing real numbers and natural numbers when he was doing no such thing. Instead, he was comparing two different bases. Only problem is that he did not realize that enumerations also have a base. For this reason, the process of creating a diagonal is flawed.

One thing to remember when you create a diagonal is that both axis must be the same. If they are not, then you are skewing the results. Cantor completely disregards any notion or attempt to keep both axis the same. The x axis is base 2 (or another base). However, what base is the y axis? Most people don't even bother to think of this. In fact, they reject it because they do not want to think about it.

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Cantor's Theorem (Updated)

Here is another theory that is commonly accepted, but is completely bogus. In the first part of this article, I only want to dispute the theory. The second half of this article deals with mapping natural numbers to real numbers. I'm playing devil's advocate in the second part because I actually believe that Cantor's conclusion is correct, but not the theory that he uses in trying to get there. Unfortunately, I must reject the conclusion as well for the time being.

As a quick recap, Cantor's theory says that you can't count to N2 by using N entries and N digits. So no matter how many digits you use (say X digits), you can always create a new (X+1)th number not already listed (by using the opposite of the digits in the diagonal). This is supposed to mean that the list of entries with infinite digits can never be put into a list because if you try to do so, you can create a new entry not found in said list. IOW, the number of entries will always be larger than the number of digits.

BOGUS!

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