This is vulgar.

]]>Oh I read about the neighborhoods required for local homemomorphsm and I see what you mean by D now. But I can see S1 properly embedded in C so how is it not a manifold? I can use the level sets of…

]]>S1 is a complex manifold. That’s the point I’m trying to make. Also what disc are you talking about and how is it related?

]]>There is no injective analytic map from S^1 to the disc. Maybe you’re thinking of S^2.

]]>What isnt a complex manifold? S1?

What. Did I miss something?

You can properly embed it into C with a smooth, not even just smooth, but holomorphic atlas.

Get tf o.

I need harder questions than this.

Okay you’re going to ask me which function then.

And I say the exponential function.

Qed.

]]>For instance by showing that certain proposition is undecidable in some given axiomatic system (e.g. the continuum hypothesis was shown by Godel and Cohen to be independent, and consequently undecidable in the standard ZFC axiomatic set theory)

]]>This is not how mathematics work. Just use your reasoning: how do we know what we don’t know?

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