In my understanding you use the Induction Hypothesis to back up your argument, but what doesn't make sense to me is that we use the Induction Hypothesis even though the Induction Hypothesis wasn't proven yet! How does that make any sense? The Induction Hypothesis are just claims we want to prove along with the main claim.
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So if I have a matrix and I put it into RREF and keep track of the row operations, I can then write it as a product of elementary matrices. ...
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I am asked to prove the density of irrationals in $\mathbb{R}$. I understand how to do this by proving the density of $\mathbb{Q}$ first, na...
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Can someone just explain to me the basic process of what is going on here? I understand everything until we start adding 1's then after ...
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