Real Elementary Functions are Continuous

Theorem

The elementary functions on the real numbers $\R$ are all continuous at every point of their domain.

Proof

In turn:

Real Polynomial Function is Continuous

Real Trigonometric Functions are Continuous

Real Logarithm Function is Continuous

Real Exponential Function is Continuous

It remains to show that:

All real functions that are compositions of the above

All real functions obtained by adding, subtracting, multiplying and dividing any of the above types any finite number of times

are also continuous at every point of their domain.

This needs considerable tedious hard slog to complete it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Finish}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): continuous function (continuous mapping)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): continuous function (continuous mapping, continuous map)