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| Math Central | Quandaries & Queries |
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I greatly appreciate your help and I was just wondering from your previous answer, why doesn't Cantor's cardinal numbers in set theory apply to the limit x->0, y=infinity? Thanks again for answering my math questions! All the Best, Justin |
Let me send that question back to you: why should it? In mathematics, things are only true if they have to be.
The cardinal numbers count sets, or "are" equivalence classes of sets, where sets are equivalent if there is a 1-1 pairing between their elements. As the only properties being considered are presence or absence of pairing, all other properties are implicitly irrelevant.
The "infinity" of calculus does not count a set; it has more the nature of a position or direction. So there is no reason for it to correspond in any really natural way to a cardinal number.
-RD
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