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Old 2021-01-04, 03:59   #76
SarK0Y's Avatar
Jan 2010

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Originally Posted by Dr Sardonicus View Post
(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.
Originally Posted by Dr Sardonicus View Post
(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????
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