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Continuity and Sequential Limits

Respected Sir / Madam,

I need each and every step. please explain me in detail.

In page 529 Theorem III.(I need proof). Text Book:- Taylor & Menon

Theorem: - Prove that Any Bounded subset of R has a supermium and Infimum?
I need proof.

Thank you

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Continuity and Sequential Limits are investigated.

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