Comparing sets of possible values Say $x$ is a real number, can one argue that the set of possible values for $x$ when $x &lt; 2$ is less than when $x &lt; 4$? Is this mathematically true?

One could argue that the set of possible values in the latter case contains that of the former case, plus other values. But, we are comparing infinite values.
It depends on your notion of size of a subset. If we partially order subsets of the real number using the subset relation then yes in a sense i.e. $\{x\in\mathbb{R}\mid x&lt;2\}\subset \{x\in\mathbb{R}\mid x&lt;4\}$. 

If we compare the sets in terms of cardinality, then no. They have the same cardinality. Let $A=\{x\in\mathbb{R}\mid x&lt;2\}$ and $B=\{x\in\mathbb{R}\mid x&lt;4\}$. The map $f\colon A\to B$ given by $f(x)=x+2$ is a bijection. 

If we compare using Lebesgue measure, then no. Both sets have measure equal to $\infty$.
mathematicaly a real line R is isomorphic with the interval $(0,1)$. I mean they have the same cardinality. can you imagine that??