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Sometimes I have trouble formulating a mathematically rigorous way of putting a proof even if I seem to understand the concept and can explain it in words. To demonstrate what I mean here is an example:

Let f(x) and g(x) be two continuous function on x in [a,b] then prove:

max[ f(x) on [a,b] ] + max[ g(x) on [a,b]] >= max[ [f(x)+g(x)] on [a,b]]

Now I can easily describe in words why this is true, because unless the maximum of f and g coincide the maximum of their sum will be less then the sum of the individual maxima That is either f or g will be smaller than its true maximum in the sum. But I don't really know how to start formulating a nice pretty way of showing it that will satisfy a mathematician.

This is just one example but I tend to go into these sorts of writing arguments a lot on my hw and am worried it is not going to past muster. I'm sure my classmates have a much better grasp on it though so i think I am doing ok in the class, but I'd still like to get better.