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circle has one center

Type of Math Object: 
Theorem
Major Section: 
Reference
Parent: 
Groups audience: 

Mathematics Subject Classification

51M10 no label found51M04 no label found51A05 no label found

Comments

I'll leave this guy world editable for a while in case I missed some minor detail.

I hope that this incident sparked by Mathprof's correction brings home the point that mathematicians can take very little (if anything at all) for granted.

> mathematicians can take very little (...) for granted

By definition, only axioms definitions, and rules of inference.

> if anything at all

Unless one assumes something, one can conclude nothing.

> Unless one assumes something, one can conclude nothing.

Agreed, but my point is/was that one has to be *very clear* what assumptions are being used. You can't play the game unless you know the rules.

Along the lines of what we discussed last night, I moved the
comments about what spaces this theorem holds in to the end
in a section on generalization. The reason for this is not to
confuse beginners who may not even have heard of non-Euclidean
geometry whilst, at the same time. presenting more complete
information for the expert.

Great idea Ray. I thoroughly approve.

Warren

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