What? Of course, the sets of integers, rationals and reals respectively are not identical , but the integers are a subset of the rational and the rational a subset of the real numbers.
"In material set theories, the elements of a set X have an independent identity, apart from being collected together as the elements of X. Frequently, they are also
sets themselves.
These are also called “membership-based” set theories.
In structural set theories, the elements of a set X have no identity independentof X, and in particular are not sets themselves; they are merely abstract “elements”
with which we build mathematical structures.
ZFC is a material set theory and is the most common set theory (and foundation).
It's different in a Structural Set Theory.
Michael Shulman: "Comparing material and structural set theories"
is really nice.
https://arxiv.org/abs/1808.05204
"In material set theories, the elements of a set X have an independent identity, apart from being collected together as the elements of X. Frequently, they are also sets themselves. These are also called “membership-based” set theories.
In structural set theories, the elements of a set X have no identity independentof X, and in particular are not sets themselves; they are merely abstract “elements” with which we build mathematical structures.