>>13205843>>13205859>>13205879I have been struggling to understand the idea of "countable infinities" and have come to the conclusion that there is a logical flaw in the argument
In my understanding, infinity is unbounded and unconstrainable. By definition is is impossible to do and attempting to do so just does not make sense. As far as I can tell, the diagonal "proof" method of talking about countable and uncountable infinities starts with something along these lines:
>A priori: Infinity is unbounded.>Let us set the infinite set of integers equal to A.>Assume we can draw a line from every integer in A to some decimal point between 0 and 1. Straw man infinity?>I can find a decimal between 0 and 1 that does not have an arrow drawn to it. Look, see? I did it. I drew all the lines in my mind and there is a number on my piece of paper that doesn't have an arrow drawn to it.>Tada - I counted to infinity and found numbers missing!>Some infinities have more lines that others, thus some infinities can be counted and some cant.Ok, so this is a quite facetious, but right now it is how I understand the proof. I just don't get how so many intelligent people don't see that Cantor assumed what he was trying to prove in his premises.
I saw one explanation saying that the lines being drawn represent a function, and that there is no function that can give a 1 to 1 line from the integers to the decimals. Poppy cock. All I need to do is count the number of orders of magnitude in a number and multiply it by 10-n As there are an infinite number of integers all numbers between 0 and 1 are accounted for with a line.
But what about irrational numbers you ask? Perhaps like Pi-3=0.14159... Ok, so there is a paradox, big deal. You have two parallel lines on a plane. Which is longer? When do they meet?
This is precisely my point. Our understanding on infinity is screwy. It does not make sense because when we are speaking about it we are actually speaking about an abstraction.
