What conceptually do I need to do?
In that mapping, all numbers that aren’t 0 map to 1. All positive numbers map to 1. The solution x + y > 0 conceptually does this. It makes all positive numbers map to 1. How do we do something similar, but just with basic arithmetic?
1 is the multiplicative identity. Any number divided by itself equals one (except zero). But we can’t use fractions.
anything to the power of zero is 1. But then 0 maps to 1.
how can we check if something is positive using only addition and multiplication?
I’ve scrolled down to see further discussion.
Okay, I hadn’t considered integer division. I don’t have practise thinking about integer division so I’m gunna practise some more see if I notice anything.
3 / 6 = 0
3 mod 6 = 3
6 / 2 = 3
6 % 2 = 0
12 / 7 = 1
12 % 7 = 5
45 / 4 = 11
45 % 4 = 1
2 / 1 = 2
2 % 1 = 0
1 / 2 = 0
1 % 2 = 1
0 / 2 = 0
2 / 2 = 1
1 / 2 = 0
0 / 2 = 0
0 mod 2 = 0
0 mod 2 = 0
2 mod 2 = 0
1 mod 2 = 1
Stopping for today. Stuck here.