Equality is also needed if you want to know whether "x<y". Proof: 1) suppose you can decide whether "x<y" for all x,y. 2) Then, for all x,y you can decide whet

Equality is also needed if you want to know whether "x<y". Proof: 1) suppose you can decide whether "x<y" for all x,y. 2) Then, for all x,y you can decide whether x==y because that's just "!(x<y) && !(y<x)"