Uniform continuity

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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
 

Answers and Replies

  • #2
Math_QED
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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.
 
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thank you
 
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Math_QED
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thank you
Welcome to physicsforums btw! Hope you have a good time here.
 
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