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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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In summary, smooth infinitesimal analysis is a mathematical framework that allows for the rigorous treatment of infinitesimal quantities. It differs from traditional calculus in its treatment of infinitesimals as non-zero but infinitely small. In this framework, continuous functions are those that preserve infinitesimal quantities and are typically proven using the transfer principle. The ability to prove continuous functions in smooth infinitesimal analysis has numerous applications in areas such as differential geometry, topology, and mathematical physics.

- #1

- 49

- 3

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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Smooth is another word for infinitely differentiable, and differentiable implies continuity.Mike_bb said:

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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