Does "Liar Paradox" requires this crappy Axiom of Infinity, that "for all N there exit N+1 > N"?
Because if you don't believe Axiom of Infinity, then for some theory (or program) N, you can't construct it's Liar structure, as it would require more memory than you have physically.
Of course, jews would say, that without infinity there is no mathematics, but why do we need this jewish tendency toward abstraction and casuistry anyway? Can you show us practical usefulness of your deceptive regilious theories, jews?
Name:
Anonymous2010-12-07 21:03
Haven't you already made 2 threads to troll about this? Stop it already.
Even if our world may be finite at the fundamental level, one will use infinities to reason about many practical things. Just like one uses integrals, derivatives, induction, complex numbers, matricies, groups, and so on... to reason about both abstract and real things. You wouldn't have modern physics, electornics, and most things relying on hard sciences today without math. Let's take a simple example everyone would understand: A rectangle with a side of length one is given, the diagonal's length is square root of 2 (given pythagora's theorem). The square root of 2 is an irrational number (easily proven), thus its decimal representation is infinite and no fraction may give you its value (but you can get approximations, as in sqrt(2)-approx<e, where e is sufficiently small value representing the error that can be tolerated). Now if you were to draw such a rectangle in the real world and calculate the diagona's distance, you would get such a value that approximates sqrt(2) to a given degree. The error would depend on the granularity of the thing you used to do your measurements with. Given a smaller scale, you would get better approximations. For an infinitely small granularity, you would reach sqrt(2), or you could say that as the granularity approaches 0, the value of the length approaches sqrt(2) - the concept of limit.
Our world's discrete nature does not mean we cannot use math to obtain incredibly important results. Math can be used to analyze systems which have infinities in them, but it can also be used to deal with completly discrete systems.
If you don't want to come to terms with this, enjoy your ignorance.