# Continuity proof

Let a < b, and f : ]a; b[ in R.

Assume f is continuous at x0 in ]a; b[ and f(x0) > c

for some number c in R.

Prove that there is delta > 0 such that

f(x) > c for all x in ]x0 - delta; x0 + delta[.

Hint;

what would happen if, for every delta>0 there were xdelta in ]x0 - delta; x0 + delta[ with f(xdelta)=< c?

https://brainmass.com/math/discrete-math/continuity-proof-numbers-218223

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Proof:

From the condition, we know that is ...

#### Solution Summary

This provides an example of a proof regarding a continuous function.

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