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Mar
9
reviewed Reject Express the vector as a sum of two vectors
Mar
8
reviewed Approve How to find union and intersection of these relations?
Mar
8
reviewed Approve Ring Theory and Modules in Norm
Mar
8
comment Eigenvalues for $y''+2y'=\lambda y$
There is no way you can find a closed form expression for $\lambda$. The best way to describe eigenvalues is that they are solutions of the equation $\sqrt{-1-\lambda} = \tan\left(\sqrt{-1-\lambda}\right)$.
Mar
3
comment Trying to find a formula for the following algorithm
What you think shouldn't be correct is in fact correct. The next step is to expand into $\frac 12i^4 + \frac 12i^2$, then compute the sum $\sum_{i=1}^n$ for $\frac 12i^4$ and $\frac 12i^2$ separately.
Mar
3
comment matlab matrix error when computing norm
What is $b^5$ supposed to mean?
Feb
23
comment What to do when particular integral is part of complementary function?
There was nothing magical about the first equation. You can derive it by using the product rule of differentiation on the right-hand side. The remark about change of basis has nothing to do with the derivation.
Feb
22
comment Why does given constraint of n lift when I simplify?
Yes it seems coincidental, but it is not completely unexpected. This kind of phenomenon sometimes leads to an interesting outcome too.
Feb
22
comment Why does given constraint of n lift when I simplify?
$F(1)$ is $a_1 = a_1$, not $a_1 = 1$. $F(1)$ does not say anything about the actual value of $a_1$.
Feb
22
comment Positive partial derivatives implies monotonicity?
It does, by the fundamental theorem of calculus.
Feb
22
comment Why does given constraint of n lift when I simplify?
Just because $n > 1$ implies $F(n)$ (where $F(n)$ is a predicate with variable $n$) does not mean $F(1)$ is not true.
Feb
22
comment Why does given constraint of n lift when I simplify?
The final formula is also valid when $n = 1$.
Feb
22
comment Why does given constraint of n lift when I simplify?
I think "the constraint $n > 1$ is now lifted" means the equation is also valid for $n = 1$, but it does not mean you can use it to find $a_1$. Observe that when you plug in $n = 1$, you get $a_1 = a_1$, which is valid.
Feb
22
comment Series question with unknown limit
You should use the formula $\sum_{n=1}^N n = \frac{N(N+1)}2$.
Feb
22
answered Tips to solve an integration problem
Feb
22
comment Showing $(P\to Q)\land (Q\to R)\equiv (P\to R)\land[(P\leftrightarrow Q)\lor (R\leftrightarrow Q)]$ {without truth table}
@crash I have to thank you then :) By the way, if you are interested, you can read about the conjunctive normal form here‌​. Disjunctive normal form is essentially the same as the conjunctive normal form when you switch $\land$ and $\lor$. (By that, I mean their definitions are the same. I'm not saying that a disjunctive normal form of one sentence can be converted into a conjunctive normal form by switching $\land$ and $\lor$.)
Feb
22
revised Showing $(P\to Q)\land (Q\to R)\equiv (P\to R)\land[(P\leftrightarrow Q)\lor (R\leftrightarrow Q)]$ {without truth table}
added 20 characters in body
Feb
22
comment Showing $(P\to Q)\land (Q\to R)\equiv (P\to R)\land[(P\leftrightarrow Q)\lor (R\leftrightarrow Q)]$ {without truth table}
@crash Don't worry about the bounty. To me, the only thing that matters on this site is that it helps people learn things. And I believe my current reputation is high enough to convince people that I'm not talking non-sense :)
Feb
22
comment Showing that $f_n$ is the number closest to $\frac{1}{\sqrt{5}}(\frac{1+\sqrt{5}}{2})^n$
From Binet's formula, try to argue that the "other" term (the one that will be subtracted) has an absolute value smaller than $\frac 12$.
Feb
22
revised Showing $(P\to Q)\land (Q\to R)\equiv (P\to R)\land[(P\leftrightarrow Q)\lor (R\leftrightarrow Q)]$ {without truth table}
added 326 characters in body