Why are the higher dimensions infinitely larger?

[Kulf_Boba]

Where does it come from that the higher dimensions are uncountably infinitely larger compared to the lower ones?

 

[Greatsage13th]

Math.

 

[ActuallySpaceMan42]

Draw a square on a piece of paper, from our perspective that square is flat. But in truth it was drawn onto a 3-dimensional piece of paper, and is itself three-dimensional, having length, width, and depth.

Now take a true 2D Square, only with width and length but no depth to speak of. Now stack another one on top of it, and then another, and then another, and do this infinitely. Is this 2D Square 3D yet? No, it still has no depth.

Even if this 2D Square has infinite width and length, it will still be smaller than a spec of dust in the 3rd dimension. Cause that spec of dust has depth, and that 2D Square even if stacked on top of itself infinitely, still does not have that extra measurement.

This can be repeated to the 3rd Dimension, no matter how infinite the 3rd Dimension is, it is unable to replicate an extra measurement of space.

Put simply, the infinity of a lower dimension is infinitesimal compared to the smallest possible size of a higher dimension's additional spatial coordinate.

 

[Reiner04]

Because they are

 

[Kulf_Boba]

Draw a square on a piece of paper, from our perspective that square is flat. But in truth it was drawn onto a 3-dimensional piece of paper, and is itself three-dimensional, having length, width, and depth.

Now take a true 2D Square, only with width and length but no depth to speak of. Now stack another one on top of it, and then another, and then another, and do this infinitely. Is this 2D Square 3D yet? No, it still has no depth.

Even if this 2D Square has infinite width and length, it will still be smaller than a spec of dust in the 3rd dimension. Cause that spec of dust has depth, and that 2D Square even if stacked on top of itself infinitely, still does not have that extra measurement.

This can be repeated to the 3rd Dimension, no matter how infinite the 3rd Dimension is, it is unable to replicate an extra measurement of space.

Put simply, the infinity of a lower dimension is infinitesimal compared to the smallest possible size of a higher dimension's additional spatial coordinate.

Ah is because in that example the depth of the 2D frame is equal to 0 and the depth of the frame drawing is equal to "X" and the difference between any finite number and 0 is infinitely uncountable.

 

[Makoto500]

Me when the was.

We got the idea from real coordinate space or cartesian coordinate system.

 

[Vietthai96]

Math, Real Coordinate Space, Continuum Hypothesis, etc.....

 

[Aachintya31]

Its a mess.

 

[Greatsage13th]

Its a mess.

A big one at that. And efficiente is going to rerevise the damn thing in the future.

 

[Sharkass]

becoz its higher dimension

 

[Aachintya31]

And efficiente is going to rerevise the damn thing in the future

It makes me laugh.

 

[Greatsage13th]

It makes me laugh.

Sure does