Let S and T be subsets of R such that s < t for each s ∈ S and each t ∈ T. Prove carefully that sup S ≤ inf T.(adsbygoogle = window.adsbygoogle || []).push({});

Attempt:

I start by using the definition for supremum and infinum, and let sup(S)= a and inf(T)= b

i know that a> s and b< t for all s and t. How do i continue? , do i prove it directly starting from s< t or will it be easier to use proof by contradiction?

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# I Supremum and Infimum Proof

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