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the mathematical discipline that applies mathematical methods to the study of mathematical theories themselves.

25 votes

Don't the axioms of set theory implicitly assume numbers?

It seems that Deniz is raising a slightly uncomfortable question of whether some circularity is built into mathematical foundations. A similar common-sense circularity is what might be called the "par …
Todd Trimble's user avatar
  • 53.3k
2 votes

Embedding Theorem for topological spaces, and in general

Every $T_0$ space is, in a canonical way, a subspace of an algebraic lattice equipped with its Scott topology. Some details can be found in this nLab article. I'm not quite sure what to do with the …
Todd Trimble's user avatar
  • 53.3k