From: James Willson (jkvw3_at_yahoo.com)
Date: Mon Feb 04 2002 - 21:01:05 PST
150:7
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Perhaps the most famous fantasy maths problem is the proof that 1 = 0.
It was commonly believed for centuries, but until the groundbreaking work
of Set, all "proofs" that 1 = 0 were unsound.
Set, of course, is the discoverer of k, a fantasy number.
k is defined as 0^0. Set used this to construct the first
sound proof that 1 = 0.
k = k (all fantasy numbers equal themselves)
0^0 = 0^0 (definition of k)
1 = 0^0 (for all n, n^0 = 1)
1 = 0 (for all n, 0^n = 0) QED
This has some interesting implications.
Since 1 = k = 0, both 1 and 0 must be fantasy numbers.
Set extended this result to show that all numbers are fantasy numbers.
(This is called Set's Fantastic Completeness Theorem)
We'll use this to prove the following trivially true:
fc + rc = (f+r)c unless c is a fantasy number
Since all numbers c are fantasy numbers, the proposition reduces to
fc + rc = (f+r)c unless true
and true -> b is true for arbitrary b. QED
Set made many important contributions to fantasy maths.
All future rules will describe some such contribution.
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Rule Date: 2002-02-05 08:51:33 GMT
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