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Jan
20
comment Where is the form $f(g(x))g'(x)$?
"entire books published consisting mainly of page after page of worked-out integrals" - Do you mean tables of integrals or books that show how to compute each integral? (Like Edward's Integral Calculus)?
Jan
20
comment Where is the form $f(g(x))g'(x)$?
@AndréNicolas Yes, Nicolas. This is not imediatelly clear from the calculus textbooks. I'm trying to understand it a little better.
Nov
29
comment Is $-2 h \sin (\theta ) \cos (\theta )\neq -h\sin (2\theta)$?
Oh, sorry. I usually assume I screwed everything up. Now I screwed up by assuming that I always screw thing up. That's a whole different plane of existence!
Nov
22
comment Why does this matrix give the derivative of a function?
@nbubis is a Jordan block and f a function matrix ?
Nov
21
comment How did mathematicians decide on the axioms of linear algebra
How does your intuition says that $c\langle u,v \rangle=\langle cu,cv\rangle $? Take the vectors $\{(a,b), (c,d)\}$, then: $e (a,b) =(ea, eb) $ and $\langle (ea, eb), (c, d )\rangle = ea\cdot c +eb\cdot d = e (ac + bd) $.
Nov
19
comment What is the meaning of primes here?
Oh, in Portuguese, they call it "linha' (line). I always thought it would be "x line" in English.
Nov
13
comment Archimedean integration of $x^3$?
@Peter Yes. A typo. I'll correct it. And I guess it's cheating because Archimedes didn't have exactly the notion of a limit. Besides, Apostol doesn't use it.
Oct
12
comment Is my proof of $-(-a)=a$ correct?
Is it too problematic to work on a representation? I wrote some ideas on a paper that was intended to teach mathematics. My goal was to bring up the idea of equivalent rewritings, loosely based on this. So these naive rewritings became my media for doing proofs in mathematics and for the first time I had a deeper access to mathematics. I guess I was following something like the formalist school.
Oct
12
comment Is my proof of $-(-a)=a$ correct?
I don't get it. Suppose the scenario you proposed: $a+A=0$. How would you do from here?
Oct
12
comment Is my proof of $-(-a)=a$ correct?
Good point. I'll think about it.
Oct
12
comment Is my proof of $-(-a)=a$ correct?
You mean theorem 1.2?
Oct
12
comment Is my proof of $-(-a)=a$ correct?
If I have $a$ and it's inverse is $-a$, then It seems natural to expect the inverse of $-a$ to be $-(-a)$. That's what I meant with "packing with a minus sign".
Sep
11
comment Proof: There is no bijection from $P(S)\to S$?
@Wojowu When he created $F$. There are too many propositions and it confuses me.
Sep
8
comment Prove that $-3/2\leq\cos a + \cos b + \cos c\leq 3$?
Perhaps it's in 3 dimensions? The book doesn't make that very clear.
Sep
8
comment Prove that $-3/2\leq\cos a + \cos b + \cos c\leq 3$?
@AdityaDev Angle between the vectors $u,v$.
Sep
8
comment Prove that $-3/2\leq\cos a + \cos b + \cos c\leq 3$?
@mastrok In the plane.
Sep
8
comment Prove that the biscetors of adjacent suplementary angles are perpendicular?
I still don't understand it, why did you omit the sum and subtraction of $A'$ for each vector? See: $$C=\cfrac{1}{2}(B'-A')+A'\quad \quad \quad D=\cfrac{1}{2}(B'+A')-A'$$
Sep
8
comment Prove that the biscetors of adjacent suplementary angles are perpendicular?
@GAVD Why didn't you add and subtracted $A'$?
Sep
2
comment Given the tetrahedron $OABC$, find a condition on $a OA+ b OB + c OC$ such that this is always inside $ABC$.
@corindo Thanks. But why is that condition true? I've been trying to prove it but have no success until now.
Aug
31
comment What's the necessary condition for that any three vectors are parallel to the edges of a triangle in the plane?
What do you mean with $\overrightarrow{AB}\times\overrightarrow{AC}\neq0$? Inner product?