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## Summary:

- I need help in order to demonstrate a formal and rigorous proof that given a real function f is continuous that ##f^+## is also continuous ... ...

## Main Question or Discussion Point

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ...

I am currently reading Chapter 3: Continuous Functions on Intervals and am currently focused on Section 3.1 Limits and Continuity ... ...

I need some help with the proof of Corollary 3.13 ...

Corollary 3.13 reads as follows:

Can someone help me to prove that if ##f## is continuous then ##f^+ = \text{max} (f, 0)## is continuous ...

My thoughts are as follows:

If ##c## belongs to an interval where ##f## is positive then ##f^+## is continuous since ##f## is continuous ... further, if ##c## belongs to an interval where ##f## is negative then ##f^+## is continuous since ##g(x) = 0## is continuous ... but how do we construct a proof for those points where ##f(x)## crosses the ##x##-axis ... ..

Help will be much appreciated ...

Peter

I am currently reading Chapter 3: Continuous Functions on Intervals and am currently focused on Section 3.1 Limits and Continuity ... ...

I need some help with the proof of Corollary 3.13 ...

Corollary 3.13 reads as follows:

Can someone help me to prove that if ##f## is continuous then ##f^+ = \text{max} (f, 0)## is continuous ...

My thoughts are as follows:

If ##c## belongs to an interval where ##f## is positive then ##f^+## is continuous since ##f## is continuous ... further, if ##c## belongs to an interval where ##f## is negative then ##f^+## is continuous since ##g(x) = 0## is continuous ... but how do we construct a proof for those points where ##f(x)## crosses the ##x##-axis ... ..

Help will be much appreciated ...

Peter