Bounded Set Contains Sequence Converging to its Supremum | Real Analysis

[@WrathofMath]

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[@tritskask2719]

That theorem can be used directly to proove the Bolzano-Weierstrass theorem regarding the bounded set as the original bounded sequence and the converging sequence as one subsequence

[@physicsul9358]

Thanks for this great explanation. Can you explain the real valued function

[@WrathofMath]

Thanks for watching! I'm not sure what you mean. What real valued function are you asking about? Or are you asking about the definition of real valued functions in general?

[@physicsul9358]

@@WrathofMath I'm asking about the definition of real valued function and about the limit and continuity of function and interval value theorem and some other properties about function...