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Apr
6
asked How to know when to use $P(x)\wedge Q(x)$ and when to use $P(x)\to Q(x)$?
Mar
31
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.
Mar
29
accepted How do the floor and ceiling functions work on negative numbers?
Mar
28
accepted Proof by induction: Show that $7|5^{2n}-2^{5n}$
Mar
28
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 $2^{5n+5}$
Mar
28
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.
Mar
28
asked Proof by induction: Show that $7|5^{2n}-2^{5n}$
Mar
28
asked How do the floor and ceiling functions work on negative numbers?
Mar
28
accepted How to reduce a congruence to a “unique” solution?
Mar
28
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
Mar
28
asked How to reduce a congruence to a “unique” solution?
Mar
28
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?
Mar
27
asked How to find the inverse of a function $f:\mathbb{Z}_{30}\to\mathbb{Z}_{30}$ defined by $f([a])=[7a]$
Mar
22
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.
Mar
21
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.
Mar
21
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.
Mar
20
asked Finding the inverse of a function
Mar
19
accepted Is the set of natural numbers closed under subtraction?
Mar
19
accepted What exactly is a lattice? And can somebody give an example of something that is not one?
Mar
19
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 :)