How many 2D objects fit into a 3D object?

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Hoe many times can you stack 2D objects before it becomes 3D? I assume stacking 2-dimensional planes alone the 3rd dimension would never actually stack, as along the 3rd dimension, the 2-dimensional planes have a thickness of 0 so i assume adding 2 dimensional objects is like adding 0s so is it technically possible for a set of 2-dimensional objects to be qualitatively similar in size/volume to a 3d object? would an uncountably infinite amount of 2D be enough to reach 3D? or is it simply not possible?

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In pure measure terms, the thickness of a 2D object is zero, and stacking any finite (or countably infinite) number of them together does not change this.

Integral calculus sort of treats a 3D object as being made of (uncountably) infinitely many 2D slices, just as it treats 2D graphs as being made of 1D line segments, but this mostly comes from starting with slices of non-zero thickness and looking at what happens as that thickness shrinks to zero.

There's also something called a "space-filling curve", in which you can describe a function that draws a 1D curve that nevertheless fills a 2D space, or any step up from there that you might consider. However, these kinds of curves are usually considered "pathological" because they lack a lot of the nice behaviour that we normally attribute to curves of their dimension.

So to put it simply, "infinitely many, one, and/or the question doesn't actually make sense"