I think I gave a counterexample... but I thought of another. A point in space. We can obviously comprehend a point.. however it is undefined because it's one of the basic assumptions of mathematics. And some assumptions cannot be proved or defined in the same system.
Exactly... however x/x when x is really big is infinity/infinity. Same for (2x)/x. When x is really big (infinitely big).. it's infinity/infinity. So how does infinity/infinity = 1? Please Register or Log in to view the hidden image!
Go with that. But it might start another argument Please Register or Log in to view the hidden image!
if 2x is infinite then it is no longer 2x but infinity. What is infinity divided by infinity? Most people would say it equals one. (infinity)x(infinity)=(infinity), so (infinity)=(infinity)/(infinity). Depending on how you figure it out, you can get infinity divided by infinity to equal just about anything. http://www.newton.dep.anl.gov/askasci/math99/math99198.htm if the above is true then infinity/infinity equals 1 or 150 billion, take your pick.
... Look... (2x)/x 1) 2/1 = 2 2) 2*2/2 = 2 3) 2*1000/1000 = 2 infinity/infinity is undefined because there is not enough information to give it a quanity. I would still like to see why infinity/infinity = 1 according to you.
http://mathforum.org/dr.math/faq/faq.divideby0.html According to this site anything using two infinities or an infinity and a zero are , as Absane has said.
Yep. Misread. The only time a + causes problems is when one of the infinities is minus infinity, effectively making it - rather than plus anyway. And of course a + or - with a zero either side is no problem. infinity + infinity = infinity But does that change the type of infinity? Countable to uncountable, or not? infinity*infinity = infinity Same with this one. 0 + 0 = 0 0*0 = 0 These don't count, since I said two infinities or an infinity and a zero. Please Register or Log in to view the hidden image!
Nope. A bad way to say this but: to make an infinity "bigger," you got to put infinity with another infinity an infinite number of times. It's a really bad way to say it... but I don't feel like getting technical. I misread, too.
Yep. Got you. Although most of my knowledge of infinities in maths comes from Ian Stewart's books and Rudy Rucker's White Light - you ever get a chance to read that (science fiction but using a ton of transfinite maths comcepts as part of the "in joke"), grab it. It's late guy. I'm calling it a night (6:40 in the morning). Catch you later.
from the site i gave earlier: Depending on how you figure it out, you can get infinity divided by infinity to equal just about anything.
