A bad mathematician's proof:
(Sorry I will have to spell all this out, can't use proper math
symbols without resorting to non-ascii messages!)
Let S be the set of all statements. Let T be the set of all true
statements. Let C be the complement of T in S. (Note that I am
deliberately not using the word "false". C includes all statements
which are indeterminate as well as false statements.)
Consider:
(1) Both this statement and statement (2) (below) are members of
C.
(2) There are an (in)finite number of primes.
Now, (1) asserts that (1) is in C. Therefore (1) cannot possibly be in
T.
If (2) is also in C, then (1) and (2) are both in C, making (1) true.
Contradiction.
Therefore (2) is true.
Clearly this is bunkum, since the wording of (2) could be changed
to anything at all without affecting the proof. However, it does help
make clear just how careful one needs to be with analytical proofs!
Regards
Brian Beesley
Regards
Brian Beesley
