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I think this is very fundamental property of real numbers, as it allows us to discuss about limits. I do not know, how the limits are playing an important role to complete the following one. Please explain.

" Any non-empty set of real numbers which is bounded above has a supremum"

This is available in standard books. But, how to complete the proof of the cited above statment by introducing LIMITS, I don't know. Advanced thanks to MSE members, who can help me.

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