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Question Number 55633 by gunawan last updated on 01/Mar/19

$$\mathrm{Known}\mathrm{set}A\subseteq \mathbb{R}\mathrm{not}\mathrm{empty},$$$$\mathrm{If}\mathrm{Sup}A=\mathrm{Inf}A,\mathrm{then}\mathrm{set}A\mathrm{is}..$$

Answered by arcana last updated on 18/Jun/19

$$\mathrm{definition}$$$$\mathrm{\forall }x\in \mathrm{A},\mathrm{Inf}\mathrm{A}⩽x⩽\mathrm{Sup}\mathrm{A}$$$$\mathrm{for}\mathrm{hip}.\mathrm{Inf}\mathrm{A}=\mathrm{Sup}\mathrm{A}=x$$$$\mathrm{hence}\mathrm{Inf}\mathrm{A},\mathrm{Sup}\mathrm{A}\notin \mathrm{A}\vee \mathrm{Inf}\mathrm{A},\mathrm{Sup}\mathrm{A}\in \mathrm{A}$$$$\text{You can't use 'macro parameter character \#' in math mode}$$$$\mathrm{A}\mathrm{is}\mathrm{puntual}$$

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