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### SuperSheep's blog

By SuperSheep, history, 7 weeks ago,

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!

• 0

 » 7 weeks ago, # |   0 Auto comment: topic has been updated by SuperSheep (previous revision, new revision, compare).
 » 7 weeks ago, # |   0 Just read the definition of ceil and floor.
 » 7 weeks ago, # |   0 it's just simple math, im assuming all the variables here are int, therefore automatically rounded down, when you divide a by b, and a % b != 0, the result gets rounded down to the integer part
 » 7 weeks ago, # |   +6 If $kx\leq y$, then $x\leq\frac yk$. By the definition of floor, the largest integer less than or equal to $\frac yk$ is $\left\lfloor\frac yk\right\rfloor$ so if $x$ is also an integer then $x\leq\left\lfloor\frac yk\right\rfloor$.