How to Prove That in Smooth Infinitesimal Analysis That Every Function on R Is Continuous?

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Mike_bb
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Hello.

How to prove that in smooth infinitesimal analysis every function on R is continuous? (Every function whose domain is R, the real numbers, is continuous and infinitely differentiable.)

Thanks.
 

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fresh_42
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Hello.

How to prove that in smooth infinitesimal analysis every function on R is continuous? (Every function whose domain is R, the real numbers, is continuous and infinitely differentiable.)

Thanks.
Smooth is another word for infinitely differentiable, and differentiable implies continuity.
 

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