Global Maxima of $x^2$ (can infinity be the maxima?) Wolfram defines Global Maxima as :

A global maximum, also known as an absolute maximum, the largest
  overall value of a set, function, etc., over its entire range.

As per the definition, I'm not sure if $\infty$ can be considered as the global maxima for functions like $x$, $x^2$, etc. What if we consider the extended real number set? 

You've probably found that when you write infinity in interval notation, you are instructed to write for example $$ y\in [0,\infty) $$
Note how the high bound infinity is not included.  This is because infinity is a boundary not a real number,
$$\infty \not\in \mathbb{R}$$
that is a number can approach but not touch infinity, so it could not be that the maximum is infinity.
