Numerically,

wondering if there are design implications to or via defining integers (1,12) as

let mod(1)=0, 0<x<=12

as opposed to 

let mod(1):=0, 0<x<=12

or

0<x<=12, let mod(1)==0

I think I mean mathematically, since none are anything more than Haskell pseudocode.

Possibly this makes only metaphorical sense.

Thanks in advance.

Alfred.