My question is what constitutes a mathematical proof?
I ask because I am currently doing a Calculus course in University and I am constantly confused regarding what I'm allowed to assume within a proof. Here is an example:
f(x) = sqrt(|x| + x^2) is continuous in Real numbers"
And the "proof" from our math book: "f is continuous, because we may present it as a union of continuous functions
h(x) = |x| + x^2 and
g(y) = sqrt(y)" Why are we allowed to assume that h(x) and g(y) are continuous? I know it's fairly obvious that they are, but it's also fairly obvious that f(x) is continuous. Yet we cannot simply assume that f(x) is continuous.