Proving Uniform Continuity of f+g with Triangle Inequality

[sergey_le]

Homework Statement

I didn't understand what I was supposed to write here

Relevant Equations

I didn't understand what I was supposed to write here

I came across the following question:
If g and f are uniform continuity functions In section I, then f + g uniform continuity In section I.
I was able to prove it with the help Triangle Inequality .
But I thought what would happen if they asked the same question for f-g
I'm sorry if my English isn't good and you don't understand me

 

[member 587159]

Nothing should change to your proof. Check that up to minor modifications the same proof still works.

Alternatively, if you have proven that if $f,g$ is uniformly continuous, then also $f+g$ you can proceed as follows.

Show that $h:= -g$ is uniformly continuous (this will follow because $|-x| = |x| \forall x \in \mathbb{R}$ if you do the proof) and then you can apply what you already proved: $f+h = f-g$ will be uniformly continuous.

 

[sergey_le]

thank you

 

[member 587159]

thank you

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