Undergrad Proving Continuous Functions in Smooth Infinitesimal Analysis

[Mike_bb]

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.

 

[fresh_42]

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.