You're working within Euclidean geometry. Space is discrete, not continuous, so there are no "squares" that have a distance of 1 unit.
Create a square on your computer screen. You'll see it's composed of a countable number of units (pixels).
Post by twetch#3375
Space is not discrete in Euclidian geometry.
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- 662 221
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- 13bJsMyjiNF21qYTLK5tZizwEovpT6DNeu
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- twetch
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- post
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- twetch#3375
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13bJsMyjiNF21qYTLK5tZizwEovpT6DNeu VerifiedReplies (3)
I know. I'm saying you are working within Euclidean geometry when you ask about the diagonal of a square with a side the length of 1.
I'm saying that no spatially-extended square has a side the length of 1, since actual squares are composite objects.
In discrete space (in the real world), units of length refer to spatially-extended points. When we say "That square has a side whose length is 9", that means "there are 9 units which compose its side."
So, you can't have a composite object made of 1 unit.
One more time, just to rephrase it:
"The diagonal of a square whose side has a length of 1" is a Euclidean object.
There are no Euclidean objects in non-Euclidean space.
All actually-existing space is non-Euclidean.
Therefore, there is no such diagonal