Does Infinity Exist?Date: 11/15/2001 at 03:24:49 From: Muhammad Arshad Subject: Infinity We talk about infinity all the time, and use it as well. What proof do we have that infinity actually exists? Even our universe is said not to be infinite, but for convenience we sometimes assume it to be, where applicable... Date: 11/15/2001 at 12:29:22 From: Doctor Peterson Subject: Re: Infinity Hi, Muhammad. What do you mean when you say that infinity exists? In mathematics, we do not treat "infinity" as a number, though it is often used that way informally. Rather, we say that something is "infinite," which simply means that it is unbounded or unlimited or unending. (That is what the Latin word from which we get the English word means.) There is no object called "infinity" that you can point out. What you are really asking is, how do we know that any particular entity has no end? The answer depends on the entity you are talking about. In mathematics, we deal only with abstract entities like the whole numbers or integers, and by definition those are infinite, just because there is nothing in our definitions that makes them stop. This doesn't mean that all of the infinitely many possible numbers can ever be used; on the contrary, it says that no one can ever use up all the numbers, even if time does go on forever. Similarly, in geometry we are dealing with an ideal plane or space that has no limits; this has nothing to do with whether actual space ends, or curves back on itself, or whatever. For practical purposes even in physics, we usually think of space as flat and unbounded; but if you are working on a problem in relativity where you go beyond small spaces and speeds, you have to start taking curvature and possible limits into account. So infinity in physics usually results from ignoring parts of reality in order to have a manageable abstraction to work with; in math it results from not caring about the real world itself in the first place. So how do we prove that "the infinite" actually exists? It exists _by definition_, but only in my mind. "I think it, therefore it exists." If you want to know whether anything in the _real world_ is infinite, you have to ask a physicist - or, better, a theologian, since I don't think science could ever prove that anything is true beyond the bounds of what we can observe. See these Dr. Math FAQs for more on these ideas: Large Numbers and Infinity http://mathforum.org/dr.math/faq/faq.large.numbers.html Dividing by Zero http://mathforum.org/dr.math/faq/faq.divideby0.html - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/dr.math/