Tuesday 12 March 2013

elementary set theory - Are the sets $mathbb{R}$ and $mathbb{R}_{>0}$ equinumerous?

Are the sets $\mathbb{R}$ and $\mathbb{R}_{>0}$ equinumerous, so is there a bijective function between these sets? And what's the best way to find such a function if it exists?

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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}...