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.
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