agent154
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 Mar31 comment Show that $\displaystyle\int_{-\pi}^\pi\sin mx\sin nx d x=\begin{cases}0&\text{if }m\neq n,\\\pi&\text{if }m=n\end{cases}$ using integration by parts @DonAntonio I accepted a solution a couple of weeks ago... It was the right one. I didn't open the bounty; somebody else is looking for an alternate solution to the one I accepted. Mar29 accepted How do the floor and ceiling functions work on negative numbers? Mar28 accepted Proof by induction: Show that $7|5^{2n}-2^{5n}$ Mar28 comment Proof by induction: Show that $7|5^{2n}-2^{5n}$ OK, I think I see where I messed this up - I did the algebra wrong when I let $n=k+1$... I had set $2^{5n}$ to $2^{5n+2}$ instead of $2^{5n+5}$ Mar28 comment Proof by induction: Show that $7|5^{2n}-2^{5n}$ @TaraB I have to do it by induction though; It's an assignment question that says as much. Mar28 asked Proof by induction: Show that $7|5^{2n}-2^{5n}$ Mar28 asked How do the floor and ceiling functions work on negative numbers? Mar28 accepted How to reduce a congruence to a “unique” solution? Mar28 comment How to reduce a congruence to a “unique” solution? It might very well be... but I'm not thinking straight right now due to panic over upcoming exams. Or maybe I'm overthinking things. Thanks :P Mar28 asked How to reduce a congruence to a “unique” solution? Mar28 comment How to find the inverse of a function $f:\mathbb{Z}_{30}\to\mathbb{Z}_{30}$ defined by $f([a])=[7a]$ I'm sorry - I really can't follow what you're saying here with all the implications on one line. Can you break them up maybe by putting the implications one line at a time like I did in my above example? Mar27 asked How to find the inverse of a function $f:\mathbb{Z}_{30}\to\mathbb{Z}_{30}$ defined by $f([a])=[7a]$ Mar22 accepted Show that, if $f:A\to B$ is a function, with $A$ and $B$ being finite sets, and $|A|=|B|$, then $f$ is one to one iff $f$ is onto. Mar21 comment Show that, if $f:A\to B$ is a function, with $A$ and $B$ being finite sets, and $|A|=|B|$, then $f$ is one to one iff $f$ is onto. I always forget that indirect proof, or proof by contradiction is a method to use... I always end up trying to go for a direct proof. Mar21 asked Show that, if $f:A\to B$ is a function, with $A$ and $B$ being finite sets, and $|A|=|B|$, then $f$ is one to one iff $f$ is onto. Mar20 asked Finding the inverse of a function Mar19 accepted Is the set of natural numbers closed under subtraction? Mar19 accepted What exactly is a lattice? And can somebody give an example of something that is not one? Mar19 comment What exactly is a lattice? And can somebody give an example of something that is not one? Thanks. Never considered this. This is why I need to study more :) Mar19 accepted Let $A$ and $B$ be arbitrary sets. Show that $|A\times B|=|B\times A|$