Monday, 17 April 2017

discrete mathematics - Why relations are defined as the smallest

Often relations are defined as follows:



The xxxxx relation is the smallest relation satisfying...


My question is why relations are defined as the smallest relations. I thought it may be so relation is uniquely defined but I have never see a proof that there is exactly one smallest relation. Does such proof exists? Are there any other reasons?

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real analysis - How to find $lim_{hrightarrow 0}frac{sin(ha)}{h}$

How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...