Floor simplification using assumptions

Question

I don't understand why Mathematica doesn't simplify these expressions:

$Assumptions = Element[x,Integers] && x>=0;
Floor[x]
Floor[9/10 + x]

The ouput is:

Floor[x]

Floor[9/10+x]

And I would like it to use the assumption and return:

x

x

Answer 1

It seems this works when you use FullSimplify:

FullSimplify[Floor[9/10 + x], Element[x, Integers]]

Btw, as soon as you use $Assumptions you don't need to specify them and you can simply call Simplify or FullSimplify.