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questions
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Proving (rigorously) that the number of $m$ element subsets of an $n$ element set is ${n \choose m}$
I am trying to solve the following problem (Amann & Escher Analysis I, Exercise I.6.3):
Show that the number of $m$ element subsets of an $n$ element set is ${n \choose m}$.
I emphasize that the ...
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3
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1
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Showing that the natural numbers are totally ordered with respect to set membership
Working with the usual set theoretic construction of the natural numbers, denoted $\omega$ for now.
I am trying to show that $\omega$ is totally ordered with respect to set membership, that is, $n<...
- 3,612
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How should we parse this proof that every infinite set has a subset which is eqivalent to the set of natural numbers?
This is again from the chapter Construction of the System of Real Numbers in The Fundamentals of Mathematics, Volume 1. It may be the case that the original wording in the German language would be ...
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