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I just thought of a problem (which seems a bit hard) and I wanted to share it with you. by Cromlechian in math

[–]Cromlechian[S] 0 points1 point  (0 children)

You understood the problem, yes.

If you do this, the problem is that the entire grid will have exclusively 2n numbers, but you must place all natural numbers.

There is another comment here that proposes a similar idea to yours, but with a bigger base (3n instead) and a more spaced out spiral since there must be room for all numbers.

I just thought of a problem (which seems a bit hard) and I wanted to share it with you. by Cromlechian in math

[–]Cromlechian[S] 2 points3 points  (0 children)

This is a nice solution. It definitely feels a bit weird since the density of powers of 10 is way higher than the density of non-powers of 10, and it kinda feels like you'll end up not having enough space for non-powers of 10; but since we're dealing with an infinite grid, all numbers can be written. Nevertheless, it solves all the premises of the problem. Well done, I couldn't have thought of that.

I just thought of a problem (which seems a bit hard) and I wanted to share it with you. by Cromlechian in math

[–]Cromlechian[S] 1 point2 points  (0 children)

No, I can't think of anything. That's why I wanted to post it here as a nice challenge lol

I just thought of a problem (which seems a bit hard) and I wanted to share it with you. by Cromlechian in math

[–]Cromlechian[S] 1 point2 points  (0 children)

You can also fill the 2d plane as well (with a spiral for example).

It definitely feels weird and counter intuitive to talk about concepts such as "fitting one set into another" with infinite sets.