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# Infinite Number is Impossible

A reader recently sent me some thought provoking ideas about infinity, and I would like to share one of them.

Assume for a moment that there are an infinite number of apples. Can another apple be added to this infinite amount of apples?

WARNING: This is a trick question for two different reasons.

First, if you have an infinite number of apples, then you have all the apples in existence and more. Therefore, it is impossible to have another apple that is not part of the infinite number of apples. So, it is impossible to add a non-existent apple to an infinite number of apples.

Second, infinite is not a number. Therefore, it is impossible to have an infinite number of apples. For that matter, it is impossible to have an infinite number of any objects, concepts, or units; including apples, millimeters, atoms, and even time.

As a result, the following equation is impossible,

∞ units + 1 unit = ∞ units

On the other hand, infinity without units can be summed. So, the following equation is valid.

∞ + 1 = ∞

I hope this is clear and easy to understand.

by Phil for Humanity
on 07/17/2013