Jason (jcreed) wrote,


I think, for A,B,Z in Sets, with A, B subset Z:
A intersection B in Z =~ limit of A >-> Z <-< B
A union B in Z =~ colimit of A >-> Z <-< B

Oh, wow. A really clever argument demonstrating
that there are continuum-many continuous functions,
heard in Set Theory today:
For continuous functions, restriction to *Q is
injective -- this follows directly from the definition
of continuity. Hence |*Cont| <= |*R^*Q| = |*R^*N| = |*R|.
But trivially |*R| <= |*Cont| because of constant
funcitons. So |*R| = |*Cont|.

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