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Why is higher-dimensional space in comparison to lower-dimensional space treated as beyond infinitely greater in size and quantity?

I'm pretty sure it's because powerscalers use higher dimensions from mathematical dimensional theories.
 
Yeah, set theory and continuum hypothesis that is: a 1D line is made up from uncountable infinite points, then 2D plane is made up from uncountable infinite 1D line, then 3D cube is made up from uncountable infinite 2D plane, from there we go further to 4D, 5D.....in order to +1 more dimensions you need uncountable infinite amount of the current one, so thus mean higher d mean higher infinity
 
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