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2021-01-04, 03:59   #76
SarK0Y

Jan 2010

2×43 Posts

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 power-of-ten 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 (not-A). 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 $p,q \in \mathbb{N}\; \frac{p}{q}=\epsilon,\; p=\epsilon\cdot q$ everything looks fine out there, right? But we have the damn grave problem, even two ones...
$p=\epsilon\cdot q$ exists everywhere for any p & q. second form has two troubling cases == 1st one w/ q = 0 and 2nd one is that..
$\displaystyle \lim_{q \to \infty}\lim_{p \to \infty}\frac{p}{q}\eq????$