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.
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