User blog comment:P進大好きbot/New Issue on Traditional Analyses/@comment-34422464-20190828003038/@comment-39541634-20190828200500

The problem is that the difference between a 4D shape and its 3D projection is obvious. You can immediately see why the latter is "smaller" than the former.

A better analogy might be a hologram: If you cut a hologram in two, you don't get half the picture. You get the entire picture, only fuzzier.

The same is true with the mathematics of infinities.The general "shape" and "size" of infinite objects does not change when they are modeled by set theory. It just becomes fuzzier.

As a simple example, the vast majority of the numbers between 0 and 1 cannot be described by any mathematical expression. Such numbers are forever outside our grasp as individual entities, yet we can easily talk about specific sets that contains them (e.g. "the set of all real numbers between 0 and 1").