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Jul
19
comment Solving recurrence $T(n) = T(\lceil n/2 \rceil) + T(\lfloor n/2 \rfloor) + \Theta(n)$
@IntrepidTraveller: We are considering a mathematical recurrence, it could be space/time complexity or even something else (like number of comparisons). Besides, we can replace $T$ in the above post with $G$ where $G(n) = T(n) - T(1)$ and for that $G$, $G(1)$ is indeed $0$. $T(1) = 0$ is taken to simplify the math, and does not change the end result.
Jun
9
comment How do I solve inequalities of the form $\left|\frac{f(x)}{g(x)}\right| \geq 1$?
@StevenGregory: You can. Notice the absolute values...
Jun
9
comment If $A,B,C,D$ are complex numbers on the unit circle with $A+B+C+D=0$, then they form a rectangle
@YotasTrejos: It is not a square. Basically, given $A$, you just reflect it along x and y axis, and then take the negative to get the four corners of the quadrilateral. Now take $A$ close to the y axis and far far away from the x axis. Do you still get a square?
May
4
comment $g^q-q$ and $g^q-gq$ are primitive roots modulo $q^2$
Using $g$ and $q$ is confusing!
Apr
26
comment Reduction from Hamiltonian cycle to Hamiltonian path
@graphtheory92: Seems valid to me. What are your concerns?
Apr
17
comment Proving that $\lim_{n\rightarrow\infty}n(a_{n+1}-a_{n})=1 \implies a_n$ diverges to $\infty$
Please use more informative titles.
Apr
17
comment How can I find if $\sum_{n=1}^\infty {n! \over 10^n} $ converges or diverges?
Please use more informative titles. The previous title you had, was on par with "Help!".
Apr
17
comment Simplifying Sum
@Guest: Using binomial theorem. It is a standard technique. You don't need to know RHS for it.
Apr
16
comment Simplifying Sum
Without the algebra precalculus tag, the left side is $$\int_{0}^{1} (1-x)^n x^m \text{d}x$$ which is a Beta integral...
Mar
29
comment Diophantine system of two equations with four variables
+1: More accessible to a 9th grader, than complex numbers I suppose.
Mar
28
comment Counting the number of integers $i$ such that $\sigma(i)$ is even.
Is this an algorithm problem? Assuming it is, retagging as elementary-number-theory.
Mar
26
comment Calculation of limit without stirling approximation
A previous answer of mine proves this in a completely elementary fashion: math.stackexchange.com/a/131084/1102. Falls right out of Proposition E.
Mar
26
comment Can the sum of reciprocals of a set without density converge?
Convergence implies density is zero. See: math.stackexchange.com/questions/5932/…
Mar
19
comment Aproximation of $a_n$ where $a_{n+1}=a_n+\sqrt {a_n}$
+1: Nice.......
Mar
19
comment Aproximation of $a_n$ where $a_{n+1}=a_n+\sqrt {a_n}$
This is not pedantry. I don't think this is as trivial as you seem to be implying. Unless you have a proof, you are just handwaving. Anyway, you are free not to elaborate, and I am free to leave the downvote intact.
Mar
19
comment Aproximation of $a_n$ where $a_{n+1}=a_n+\sqrt {a_n}$
Please take at least a day or two before accepting an answer. In this case, the accepted answer is incomplete.
Mar
19
comment Aproximation of $a_n$ where $a_{n+1}=a_n+\sqrt {a_n}$
The heuristic is only a first step. Making it rigorous is the hard part. -1 till there is a proof. Sorry.
Mar
18
comment Quotient of a regular language
@AstroNauft: You don't need to determine anything. It is a non-constructive proof. $L$ could be any language.
Mar
18
comment The limit : $ \lim _{x \to \infty } \sqrt{x^2 +x} - \sqrt{x^2 +1} $
Related: math.stackexchange.com/questions/30040/…
Mar
17
comment How to show that $\lim_{n \to +\infty} n^{\frac{1}{n}} = 1$?
@ADG: It is my name, I will spell it as I want! :-). Just kidding :-). Apparently, it is actually Aryabhata and not Aryabhatta. In fact I had it as Aryabhatta till ShreevatsaR corrected me.