Cartesian Geometry beyond Dimensions.

Higher-dimensional geometry (previously "Polyshapes").

Cartesian Geometry beyond Dimensions.

Postby ubersketch » Sun Nov 18, 2018 7:53 pm

In this post I will post the concept of a mension.
To start we will introduce the unimensions.
[0][1][2][3][4]...
These are all the natural numbers.
Now onto the dimensions.
Eventually after exhausting all of those we go to the next row.
[1,0][1,1][1,2][1,3]...
And after exhausting all of those, we continue to the second row, and so on.
After exhausting all of the rows, we go to the 3rd dimension.
[1,0,0][1,1,0][1,2,0]...
We move on the the fourth dimension and so on...
Until we exhaust all of the dimensions and move on to the trimensions.
[1[1]0...]
Of course, these actually correspond to infinite ordinals.
Remember that the unimensions were natural numbers.
If you exhaust the natural numbers, you get omega or w.
All of the n-mensions have a limit of epsilon0 or e0.
Note: A [0] separator is just a comma, and any coordinates starting with 0 can have the 0 removed. Also this was inspired by Bowers' hypernomials.
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