defining infinity without headaches

having become fed up with the abuse of the word infinity in mathematics, specifically Cantor's alephs etc. I put forth a new simpler definition of Infinity, which, @ this time, is only semantically different. Think of the set of all integers as a circle. Now draw the circle reprsenting the set of all even integers. Naturally, since it is contained within the set of of all integers, the second circle will be drawn within the first. The size of the circles drawn are irrelevant and have no meaning regarding the 'size' of the sets. This notation is only for purposes of containment. On closer inspection, every set can be described as being contained within another set. My definition of infinite is this: A set is infinite when it cannot/is_not (be) contained within another set. Since there is no such set as this, infinity is ultimately unreachable yet again, and Cantor can be said to be talking about how close to infinity such sets are. 

This also achieves the result of having a single infinity towards which each of these sets is aspiring.

Thu May 4, 2000 6:40 pm