- #1
Estanho
- 14
- 2
Hi,
I've been trying to find one symmetric "injective" N²->N function, but could not find any. The quotes are there because the function I'm trying to find is not really injective, as I need that the two arguments be interchangeable and the value remains the same.
In other words, the tuple (a, b) yields the same result as (b, a), which defines simmetry, but the result of (a,b) and (b,a) should not be obtained by any other combination of arguments.
I'm also not sure how to prove if one such given function obeys this property, and this is one of the main problems, as I was able to find some that works for small numbers, but then fail with bigger ones (which makes it very hard for me to check).
If anyone could help me with this, it would be better if the output would not grow too fast.
Sorry if there any obvious candidates.
Thanks
I've been trying to find one symmetric "injective" N²->N function, but could not find any. The quotes are there because the function I'm trying to find is not really injective, as I need that the two arguments be interchangeable and the value remains the same.
In other words, the tuple (a, b) yields the same result as (b, a), which defines simmetry, but the result of (a,b) and (b,a) should not be obtained by any other combination of arguments.
I'm also not sure how to prove if one such given function obeys this property, and this is one of the main problems, as I was able to find some that works for small numbers, but then fail with bigger ones (which makes it very hard for me to check).
If anyone could help me with this, it would be better if the output would not grow too fast.
Sorry if there any obvious candidates.
Thanks