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May
19
comment Why having $ma+np=1$ implies that $m$ is the inverse?
Yes. Every multiple of $mp$ of $p$ puts $mp$ in the same class of equivalence, namely $mp=\overline{0}$, then $ma+\overline{0}=1$. I guess I get it now.
May
19
comment Why having $ma+np=1$ implies that $m$ is the inverse?
What do you mean with $[]$?
May
17
comment A silly problem on critical points?
@zhw. So those critical points are complex critical points?
May
17
comment A silly problem on critical points?
@zhw. Then why Wolfram Alpha says there are critical points?
May
17
comment A silly problem on critical points?
@John Yes. But the problem is that it seems that it's possible to do some magic and use it. Mathematica solves $\sin(x)=2$ as {{x -> ConditionalExpression[\[Pi] - ArcSin[2] + 2 \[Pi] C[1], C[1] \[Element] Integers]}, {x -> ConditionalExpression[ArcSin[2] + 2 \[Pi] C[1], C[1] \[Element] Integers]}}.
May
17
comment A silly problem on critical points?
@John From the page: "$Sin^{-1}(x)$ is the inverse sine function."
May
17
comment A silly problem on critical points?
@John See here.
May
14
comment If $n^2=ab$ and $\gcd(a,b)=1$, show that $a,b$ are not necessarily squares.
And the author actually gave a similar hint in the beginning of the questions and I completely missed it. I'm so stupid.
May
14
comment If $n^2=ab$ and $\gcd(a,b)=1$, show that $a,b$ are not necessarily squares.
Oh. $-1\cdot -1$ and $1 \cdot 1$. I guess I understand it.
May
14
comment If $n^2=ab$ and $\gcd(a,b)=1$, show that $a,b$ are not necessarily squares.
@HenningMakholm I explained a little further in the text.
May
14
comment In a ring, if addition is commutative, does it implies that multiplication is commutative?
@RobertLewis No. See my profile for explanation.
May
14
comment In a ring, if addition is commutative, does it implies that multiplication is commutative?
Of, it seems I confused one thing. Here. He says: "In addition, if $ab=ba$, then it is a commutative ring". I thought he was talking about addition. Silly me.
May
14
comment What is $R(k,l)$?
Oh, now I get it. Thanks.
May
6
comment Why can't we eliminate $t$?
@MatemáticosChibchas Yes, my child. I am very fond of this song, you should be too.
Apr
27
comment At which points the tangent lines of the function $y=\cos x$ are parallel to $-\frac{1}{2}x+1$?
@user37238 Yes! I guess you helped me to find the silly mistake. Let me write it.
Apr
27
comment At which points the tangent lines of the function $y=\cos x$ are parallel to $-\frac{1}{2}x+1$?
@user37238 When I evaluate $-\sin x=- 1/2$, I'd have the pair $(\pi/6,-1/2)$. The first item of the pair is $x$, the second one is $y$. I just made the substitution.
Apr
20
comment How to show that $0<b'<b$?
@rightskewed Yes! The condition of comparability of rational numbers. I had this insight yesterday but used in a cumbersome way that yielded nothing. Now I forgot to use it. Thanks!
Apr
15
comment About the differentiability of $|x|$?
Exactly. I was a little bit lazy when typing, sorry.
Apr
15
comment About the differentiability of $|x|$?
I made a silly mistake, my impression was actually: I am starting to guess that for a function to be differentiable at a point, all it's derivatives should also be continuous at the same point.
Apr
15
comment About the differentiability of $|x|$?
Sorry, I made a mistake, it's actually: I am starting to guess that for a function to be differentiable at a point, all it's derivatives should also be continuous at the same point.