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Old 11-05-2012, 05:35 AM   #11
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Join Date: Oct 2005
Posts: 34,387

Originally Posted by ninman View Post
The real question is, is infinity really the largest number.

For example if we call infinity - omega, then omega + 1 is bigger than omega, but still infinitely large.

If we keep going we can get omega + omega = 2omega.

Continuing we get to omega^omega, but then omega^omega+1>omega^omega.

If we keep going, we can get omega^omega^omega... - omega times. Then if we take that number +1, we get something bigger still, and start all over again.

Meaning there are infinitely many, infinitely large numbers. By this definition omega-omega=0 (I think).
+inf - (+ inf) is undefined.
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