What is Infinity?

	Duration: 1124 seconds Upload Time: 07-02-02 14:42:47 User: websnarf :::: Favorites
Description: A basic definition of what infinity is.
Comments
ThisSentenceIsFalse ::: Favorites I didn't mean infinity is not an adjective. Infinity can't be a number because it doesn't stop to be one. I meant the definition of infinity from set theory produces paradoxes.One of my favorite paradoxes is Hilbert's Hotel. Try and look it up. 07-06-29 23:21:10 _____________________________________________________
ThisSentenceIsFalse ::: Favorites Your questions are interesting to me. They are the starting points to understanding the properties of infinity. For instance that 'race track' thing touches on the distinction between potential and actual infinity. Try reading about George Cantor or Kurt Godel. They were both major mathematicians who went crazy working on infinity. 07-06-29 23:23:10 _____________________________________________________
llazyoli ::: Favorites ultrafinitism. i'd probably go with that. 07-07-01 22:06:47 _____________________________________________________
llazyoli ::: Favorites btw. there should be opportunites to see actual infinity if such a thing exists. first one should be you standing between mirrors but probably this fails because you're in the way of your own image or the angle you need can't be reached. i don't know. second one would be to film yourself live on tv. holding the camera at the screen (which shows you filming yourself, with a camera filming yourself and so on). a well known glitch or bug in many computergames (overlapping objects) also. 07-07-01 23:19:13 _____________________________________________________
llazyoli ::: Favorites i guess what you can see there is the typical pattern of fractals forming a new pattern out of existing parts and details of another structure (kaleidoscope). third maybe the feedback of a microphone. all this fails at some point due to a certain amount of imperfection. ...now i am spamming the board i guess. 07-07-01 23:20:27 _____________________________________________________
mbk181 ::: Favorites I don't know if anyone has posted this yet, but there is another definition of an infinite set. Any set which contains a proper subset of the same cardinality is an infinite set. 07-08-07 19:28:55 _____________________________________________________
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websnarf ::: Favorites Ok, but that requires that you define cardinality. 07-08-08 11:20:52 _____________________________________________________
mbk181 ::: Favorites Cardinality is the measure of the number of elements in a set. If a set is finite with n elements, we say that the cardinality of the set is n. If no such n exists for a set S, and the set is not empty, then we can find an injection f:N --> S. Since we can construct a bijection g:N\{1} --> N, we can construct a map k:S\{f(1)} --> S that gives a bijection induced by g(f). This way this def. agrees with the one you used but isn't a definition by negation. 07-08-08 12:27:58 _____________________________________________________
websnarf ::: Favorites I know what it is, but the point of my lecture is to aim it at regular non-math heads. There is no reason to avoid definitions by negation. 07-08-09 03:13:07 _____________________________________________________
mbk181 ::: Favorites Sorry, this comment wasn't really aimed at you as I agreed with most everything you said in your video, I just noticed a lot of comments below of people saying they didn't like the 'not' definition so I was giving an alternative. A lot of people say infinity may not be used as a noun on here also, which isn't true, as in the extended reals, surreals and projective spaces. 07-08-09 07:34:01 _____________________________________________________