Why are integers subset of reals? In most programming languages, integer and real (or float, rational, whatever) types are usually disjoint; 2 is not the same as 2.0 (although most languages do an automatic conversion when necessary). In addition to technical reasons, this separation makes sense -- you use them for quite different purposes.
Why did they choose to say $\mathbb{Z} \subset \mathbb{R}$ in math? In other words, why are 2 and 2.0 considered the same?
When you are working in $\mathbb{R}$, does it make any difference whether some elements, eg. 2.0, also belong to $\mathbb{Z}$ or not?

Why shouldn't we say $\mathbb Z\subset \mathbb R$?
In some cases it makes a lot of a difference to be able to conslude that some number obtainined by calculations within $\mathbb R$ is an integer as that allows us to do much more.
