(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that if a < b + ε for every ε>0 then a ≤ b

2. Relevant equations

I am not sure if this is a right way to do it? I just want to know if it does make sense

3. The attempt at a solution

proof.

a < b + ε → if a is bounded above by b+ε then b is the least upper bound for a.

which means a ≤ b.

ε is the upper bound of a since b≤ε.

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# Show that if a < b + ε for every ε>0 then a ≤ b

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