The enigma of infinity (preview)

Topics: Mathematics, Georg Cantor, Set theory Pages: 2 (462 words) Published: June 18, 2014
The Enigma of Infinity
1 denumerability of rational ‘Numbers’
To understand certain qualities of infinite one has to fathom the notion of what intrinsic values we consider numbers. “A number isn’t a number” as stated by Georg Cantor, nineteenth century mathematician. Cantor developed what is known as Cantors Theory of Sets, which states as follows, “For comparing the magnitude of two different sets, the basic notion is that of equivalence. In other words elements A and B may be paired with one another in such a fashion that A only corresponds to B and vice versa. This applies to what we call numbers, which in fact only represent the value it holds, in other words number B isn’t itself abstract as it’s the representation of element A. Outside the realm of mathematics numbers represent something, and mathematics was created to short cut the way we describe element A. Because of this we can consider what follows:

2≠3 unless, 3=2
To the average mind this will seem to be nothing but obvious, nevertheless it’s a difficult concept to understand. When furthering the Prima Facie, or face value that is present we find that this indeed is a possible impossibility. Because numbers are just representation of values and they themselves are not abstract, they can be manipulated to equal the indicated equation above, A=2 B=3 A=B, therefore 2=3

Because the elements are equivalent before the values holder are nonequivalent because elements come before their representation. However the contradictions begin to follow as to say I have A equals the number of Bananas I have in my right hand, B also equals the number of Bananas I have in my left hand. Therefore I have 3 Bananas in my left hand and 2 Bananas in my right hand, and according to premise one they are equal, however the potassium is greater in my left hand evidently. My point is numbers are what they seemed to be, for example in a sequence such as 2, 4, 6,8,10

The corresponding representation of each value...
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