What is the thickness of the infinitely superimposed planes?

Question

Geometry

What is the thickness of the infinitely superimposed planes?
If we take into account that the thickness of one plane is infinitely small tending to zero.
I apologize for not specifying: They mean in our space, but as you know, in our universe there are only Real numbers.

Answer 1

0 because they don't overlap like a stack of paper, but occupy the same coordinates. And in general, the plane has no concept of thickness.

Answer 2

There is no "overlay" of planes defined in mathematics, so the answer depends on how you define your term.
Option 1: Synonym for matched planes, then see SagePtr 's answer .
Option 2: for any epsilon>0 there is a plane parallel to the given one and separated from the given plane by epsilon. Then we obtain the filling of the entire 3-dimensional space, i.e. "thickness" is infinite.

as you know in our universe there are only natural numbers

Nice to meet you and welcome to our universe. Everything is more complicated here, there are real ones, there are complex ones, there are quaternions , etc., so be careful, for a stranger from the quiet world of natural things, there will be dangers at every step. Believe it or not, even the voltage in the outlet is not natural, not discrete, sinusoidal, although it will be difficult for you to understand for now. Well, while you get used to our universe.
PS I remembered about dinorobs from "Fuzzy crushing" :)
PPS Stop. Or in "your Universe" unit is equal to the Planck length?