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Consider the set $$A=\{\sin n:n \in \mathbb{N}\}$$ How should I proceed to prove that $\sup_{n\in \mathbb{N}} A = 1$? Is there a direct proof? Can any argument be provided via reductio ad absurdum?

William Elliot
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FreeMind
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  • I don't understand why somebody votes to close the question without even providing any argument regarding the reason to do so! This question is purely motivated from the abstract definition of supremum that I have problem understanding. – FreeMind Mar 21 '19 at 11:55
  • I know a few proofs, but no elementary ones – Jakobian Mar 21 '19 at 12:00
  • https://math.stackexchange.com/questions/63526/showing-sup-sin-n-mid-n-in-mathbb-n-1 – PierreCarre Mar 21 '19 at 12:01
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    Also see (https://math.stackexchange.com/questions/484131/what-is-sup-sinn?noredirect=1&lq=1) – Chinnapparaj R Mar 21 '19 at 12:02

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