Ordinality of a Set

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What is the difference between Ordinal number and cardinal number of a set?....I have a confusion in understanding the difference between the two.Can anyone help me to understand these two things? Thank you.

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1 Answer

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For finite sets it is the same thing, because a finite set can be well-ordered in a unique way, up to isomorphism. But for infinite sets there are many non-isomorphic well-orders that can be given to the set, but only one cardinality.

In other words, ordinals deal with structure -- order. Cardinals, and cardinality, deals with non-structure.

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