quote:1 / 0 is greater than infinity... because no matter how many times you multiply by 0 its always 0.
There is nothing greater than infinity by definition.
Also, is 1 / 0 negative infinity, because no matter how many negative times you multiply by 0, it''s always 0. Or is it a complex infinity...
Unfortunately for me:
quote: Access Denied to IP Address 203.109.249.138
----------------------------------------------------------------- Thank you for your interest in Eric Weisstein''s World of Mathematics. Unfortunately, your client, subnet, proxy, or cache server has been identified as source of an excessive number of hits which appear to have originated from a robot or spider.
That IP address is the IP address of the proxy my ISP has. Some loser just ruined one of my favourite sites for me
quote:Original post by Cold_Steel That''s true, I forgot about that. I was just thinking that there was no way to represent infinity in an integer format or something like that. IEEE floats do have an overflow or something if I recall correctly, which can be treated as infinity.
IEEE floats have positive and negative infinity. They also have denormalized numbers(underflow), NaN(Not a Number - 0/0), and other fun things.
1/0 is undefined, however the limit of 1/x as it approches 0 from either side is defined. There is a difference between the limit being defined and the number being defined, as most calculus books will tell you... Jesse
Infinity isn''t a number and applying operators to it is rubbish, infinity is more of a concept. There are different ''orders'' of infinity. It''s a useful concept, but trying to compare it with anything other than itself and ways of obtaining it is a bit of a waste of time. As for 1/0, it''s rubbish that''s all. If your in a situation where you''re trying to divide by 0, you shouldn''t be. It certainly isn''t defined, but it may not necessarily be undefined as it doesn''t exist.
eg, for f(x) = 1 / (1-x)
f(1) is undefined, not really because 1/0 is undefined, but because our definition doesn''t cover f(1).
infact that last definition is wrong, it should be:
f(x) = 1 / (1-x) x is not equal to 1
All this is a matter of definitions and different viewpoints. The one this we should all agree on is that 1/0 is not defined, for reasons argued by other people.
quote:Original post by SpaceRogue There are different orders of infinity which are not 'equal'. I've seen it proven in some of my advanced math courses.
An example of this is how the set of all real numbers is larger than the set of all integers. Even though both sets have an infinite number of members, one is larger than the other. There are varying degrees of infinity. Weird, huh?
EDIT Check out the "infinite hotel" too. It sort of illustrates this sort of thing. Really cool problem. Not sure it exactly applies though.
[edited by - Cold_Steel on April 23, 2003 8:41:59 PM]
______________________________"Man is born free, and everywhere he is in chains" - J.J. Rousseau
quote:however the limit of 1/x as it approches 0 from either side is defined. If it''s defined, what is it??? lim (x->0) |1/x| is defined to be infinity, but 1/x doesn''t have a limit at x=0.
Cédric
Ever heard of limits AT infinity? It is terminology used. Furthermore, we have to be more precise about lim x>0 (1/x). Only using a one sided limit does the limit exist. It is simply infinity. That qualifies. Such as lim x>0- (1/x) = -oo and lim x>0+ (1/x) = oo
