# Math Help - Proof of Continunity-why are taken min(1,e) to choose delta epsilon

1. ## Proof of Continunity-why are taken min(1,e) to choose delta epsilon

Prove that the function f(x) = 1/2+x is continuous at x=0.

I have attached the solution. My question is why are they choosing between minimum of epsilon and 1 for the value of delta epsilon?

Any help would be appreciated.

Thanks

2. The reason is contained in the next line after the part you underlined.
It makes the setup happen.