3 ms·
> Could this be accomplished with other bases and other number systems having more than one dimension? Yes, all sets ℤⁿ (n > 0) have cardinality ℵ₀ and therefo
by colanderman 3y ago
> Could this be accomplished with other bases and other number systems having more than one dimension?
Yes, all sets ℤⁿ (n > 0) have cardinality ℵ₀ and therefore a bijection can be defined for any set ℤⁿ↔ℤ.
The "computer science" way to think of this is, you can always e.g. interleave the bits of any number of integers, to encode them as a single unique integer. For two dimensions this is the Z-order curve [1].
[1] https://en.wikipedia.org/wiki/Z-order_curve https://en.wikipedia.org/wiki/Z-order_curve
- peter_d_sherman 3y agoNever would have thought of the relationship between this and the Z-order curve -- but yes, upon consideration, I see the relationship! Brilliant!