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Question Number 167179 by mathocean1 last updated on 08/Mar/22

$$Demonstratethat\mathrm{\forall }x,y\in {\mathbb{R}}_{+}^{\ast },\mathrm{\forall }q\in {\mathbb{Q}}_{+}^{\ast }$$ $$suchthatq>xy,\mathrm{\exists }a,b\in \mathbb{Q}such$$ $$thata>x,b>yandab=q.$$

Answered by mindispower last updated on 09/Mar/22

$$supposex<y$$ $$letI=]x,\frac{q}{y}[\ne \left\{\right\}\therefore \frac{q}{y}>x\iff q>xy$$ $$leta\in I\cap \mathbb{Q}\ne \left\{\right\}\frac{q}{y}>a>x.....\left(1\right)$$ $$y<\frac{q}{a}=b<x....\left(2\right)$$ $$\left(1\right)\mathrm{\&}\left(2\right)Giveusanswer$$ $$\left\{\right\}emptyset$$ $$$$ $$$$ $$$$ $$$$

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