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E-x-Q-x-2-gt-3-Show-that-E-has-not-lower-bound-in-Q-Montrez-que-E-n-admet-pas-de-borne-inferieure-dans-Q-




Question Number 164474 by mathocean1 last updated on 17/Jan/22
E={x ∈ Q_+ :x^2 >3}.   Show that E has not lower bound  in Q.  [Montrez que E n′admet pas de borne  inferieure dans Q]
$${E}=\left\{{x}\:\in\:\mathbb{Q}_{+} :{x}^{\mathrm{2}} >\mathrm{3}\right\}.\: \\ $$$${Show}\:{that}\:{E}\:{has}\:{not}\:{lower}\:{bound} \\ $$$${in}\:\mathbb{Q}. \\ $$$$\left[{Montrez}\:{que}\:{E}\:{n}'{admet}\:{pas}\:{de}\:{borne}\right. \\ $$$$\left.{inferieure}\:{dans}\:\mathbb{Q}\right] \\ $$

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