Expressing <= using <

Can you express a <= b using only strict less than operator?

Yes. We have a <=b <=> for all e > 0, a < b + e

Proof => Obvious!

<= Assume not. Then a > b.
Take e = a - b >0
Then by hypothesis, we have

a < b + e = b + a - b = a

Contradiction!

QED.