Quick question about floor and ceiling when dividing in an inequality

Правка en2, от SuperSheep, 2023-02-02 03:22:12

I'm aware that if $$$2x \leq y$$$ then $$$x \leq \lfloor y/2 \rfloor$$$, and that if $$$2x \geq y$$$ then $$$x \geq \lceil y/2 \rceil$$$

I usually remember that by writing examples like $$$x \in$$$ {$$$2,3$$$}, $$$y=5$$$. But I don't quite get the logic behind that and I'm not sure if it's a general rule that $$$kx \leq y \rightarrow x \leq \lfloor y/k \rfloor$$$.

Any help with understanding that or resources to read about it would be greatly appreciated. Thanks!

Теги math, inequalities, division

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en2 Английский SuperSheep 2023-02-02 03:22:12 6 Tiny change: 'ike $x \in \{2,3\}, y=5$. But ' -> 'ike $x \in$ {$2,3$}, $y=5$. But ' (published)
en1 Английский SuperSheep 2023-02-02 03:17:59 508 Initial revision (saved to drafts)