Quote:
Originally Posted by Dr Sardonicus
(1) OP seems to be confounding "fractions" (rational numbers) and "decimal fractions," i.e. fractions that can be expressed with a poweroften denominator. Not all rational numbers are decimal fractions.

don't confuse numerical system & numbers itself == any proper numerical system can express any number. Another moment is how efficient that expression could be.
Quote:
Originally Posted by Dr Sardonicus
(2) OP also seems to think that invalidating a proof of A automatically proves ~A (notA). It doesn't. (Here, A is "The square root of 2 is irrational.")

no, the very point is, you must uniform objects before you do operations on them. that proof messes w/ two different types of objects. for instance, 1/3 is odd or even? or let
everything looks fine out there, right?
But we have the damn grave problem, even two ones...
exists everywhere for any p & q. second form has two troubling cases == 1st one w/ q = 0 and 2nd one is that..