Could 2 dimensional objects fill a 3 dimensional space?

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SUMMARY

The discussion centers on the concept of whether an infinite number of two-dimensional (2D) objects can fill a three-dimensional (3D) space. It concludes that while mathematically, certain constructs like space-filling curves exist, physically, 2D objects cannot occupy a 3D volume. The distinction between mathematical theory and physical reality is emphasized, highlighting that in physics, there are no true 2D objects and no infinite quantities.

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  • Understanding of mathematical concepts related to infinity
  • Familiarity with space-filling curves in mathematics
  • Basic knowledge of dimensionality in physics
  • Concepts of 2D and 3D geometries
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  • Explore the implications of dimensionality in physics
  • Study the concept of infinity in mathematics
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Imagine if we had an infinite number of 2d objects, could they fill a 3d volume? even if there is an infinite number of them?
 
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There are no 2d objects in physics, and not an infinite amount of anything. In mathematics, it depends on the type of infinity you mean.
 
Mathematically there are space filling curves - physically no.
 
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