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Aug
24
asked $\forall a[P(a)\implies Q(a)]\wedge \forall a[Q(a)\implies P(a)]\stackrel{?}{\equiv} \forall a[[P(a)\implies Q(a)]\wedge [Q(a)\implies P(a)]]$
Aug
22
comment The method of exhaustion in tom apostol calculus vol $1$
You can skip this intro and keep reading it nonetheless. As you progress through the book, you may have developed more mathematical maturity. I tell you this because the first time I took this book, I knew very little mathematics and also found the introduction a little hard.
Aug
21
asked $1+2+3=\int_{0}^{\infty}t^3e^{-t} dt$?
Aug
18
comment On the inner workings of induction?
Good, that's the spirit. When I read about induction, everything seemed to be connected and it made no sense. After some thought, I realized that induction is one thing that can be used to prove ideas in another ideologically feasible frameworks, such as graphs, semirings (in this case), etc.
Aug
18
comment On the inner workings of induction?
No, I'm not trying to prove it's right. I'm trying to understand what are the laws that forbid me of writing $f(k+1)= f(k)+(k+1)$. And I guess it has something to do with the semiring axioms.
Aug
18
comment On the inner workings of induction?
I mean, to write $f(k+1)$ as $f(k)+(k+1)$, I need to have the idea of equivalent rewriting, and I guess this idea comes from the semiring axioms.
Aug
18
comment On the inner workings of induction?
Why doesn't induction works on semirings? After all, we're dealing with $\Bbb{N}$, addition and multiplication. And it follows these axioms.
Aug
18
comment On the inner workings of induction?
@KittyL Yes. The weird thing is that using the first $5$ numbers of that sequence, it yields preciselly the formula of the sum of the first $n$ positive integers. I'm curious about why does it gives precisely $\cfrac{x(x+1)}{2}$ and not some other random formula. But I'll ask this on another ocasion.
Aug
18
comment On the inner workings of induction?
@whacka Yes. I've also looked for some easy sequence (sharing some of the first terms) on OEIS. But as I read Farrugia's article I mentioned in the text, I had to use it because seemed fun.
Aug
18
revised On the inner workings of induction?
added 64 characters in body
Aug
18
comment On the inner workings of induction?
Sorry, @whacka. We edited at the same time.
Aug
18
revised On the inner workings of induction?
added 305 characters in body
Aug
18
asked On the inner workings of induction?
Aug
17
comment How do I prove this $\frac{dx^n}{dx}=nx^{n-1}$ is true for every $n\geq 1$ to convince my students?
@AndréNicolas That is the proof that is also given by Hairer/Wanner: Analysis by It's History. I guess that it's the less bureaucratic way to do it, since it rely only in the proof of the product rule, which is quite simple.
Aug
17
revised What's the purpose of this unknown (financial) math formula?
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Aug
17
comment Why don't we start studying calculus via series instead of the calculus on finite expressions?
@ChristianBlatter I don't get it. What's the conclusion?
Aug
16
asked Why don't we start studying calculus via series instead of the calculus on finite expressions?
Aug
15
comment Why to include the $C$ in the formula for the distance in hyperbolic geometry?
@Blue Not yet. I thought I ought to know, mainly because there is an exercise on this page.
Aug
15
asked Why to include the $C$ in the formula for the distance in hyperbolic geometry?
Aug
14
asked If $A$ and $B$ are arbitrary $m\times n$ matrices, show that $^t(A+B)= {}^tA+{}^tB$?