This re-instated what passes for faith in humanity

[--Pete]

Hi,

Just a small clarification:

Is it possible for a set that contains 100 elements, regardless of what the elements are, to not also contain 99 elements, 98, and so on?[right][snapback]98527[/snapback][/right]

The confusion here is that you are failing to distinguish between a set and sub-sets of that set. If a set is defined so that it contains 100 specific elements, then it contains those 100, no more, no less. There does exist a sub-set of that set (indeed, 100 subsets) which only contains 99 of those elements. But the sub-sets are not the original set.

As important as well defined concepts and semantics are to a reasoned mathematical argument, this point is still a quibble. Rephrased as, "Is it possible for someone to have 100 elements, regardless of what the elements are, to not also have 99 elements, 98, and so on?", your question has merit. Where it fails is not within itself, but in trying to extend such arguments to the infinite (either mathematical or philosophical).

--Pete