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1d
answered Prove that $\det(A^2 + A + xI) = x$
1d
awarded  Nice Answer
2d
answered How can I prove $\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}…}}}}=2$
Dec
21
comment Necessary and sufficient condition for the existence of $\lim_{n\to\infty} a_n$
@PseudoRandom Let me quote what my post sais: "Prove that $$\lim_n a_n$$ exists if and only if all of the following three limit exist: $$ \lim_n a_{2n} \,;\, \lim_n a_{2n+1} \,;\, \lim_n a_{3n} $$ " So I don't understand your complain. The inverse is trivial, and for the converse, the existence of the three limits is part of the statement...
Dec
21
comment Necessary and sufficient condition for the existence of $\lim_{n\to\infty} a_n$
@PseudoRandom You only read half of the paragraph, the proposition before states exactly what you said. And the proposition you quoted sais something different than what you are implying: it sais that for the proof this condition is ONLY needed to guarantee that the three limits are the same, it is not needed for anything else.
Dec
21
awarded  Constituent
Dec
13
awarded  Enlightened
Dec
13
awarded  Nice Answer
Dec
12
awarded  geometry
Dec
8
awarded  Caucus
Nov
29
comment What is the value of $a+b+c$?
@Argha If you are familiar with symmetric polynomials, they guarantee that complex solutions do exist, and you can find the cubic polynomial which has them as roots. Than you can decide if they are real or not....
Nov
29
comment What is the value of $a+b+c$?
And to prove that $x^4\equiv x^6 \pmod{2}$ it suffices to check the cases $x \equiv 0,1 \pmod{2}$. Or an overkill is to use the stronger form of Fermat Little Theorem: $$x^2 \equiv x \pmod{2} \Rightarrow x^6 \equiv x^2 \cdot x^2 \cdot x^2 \equiv x \cdot x \cdot x^2 \pmod{2}$$ Actually you can prove that $x^n \equiv x \pmod{2}$ for all $n \geq 2$.
Nov
29
comment What is the value of $a+b+c$?
@barakmanos yes. If $x$ is even $x^4, x^6$ are both even, and if $x$ is odd then $x^4$ and $x^6$ are odd. Sign is irrelevant.... Note that the solutions reduces to $x^4 \equiv x^6 \pmod{2}$ implies that $a^4+b^4+c^4 \equiv a^6+b^6+c^6 \pmod{2}$.
Nov
29
answered What is the value of $a+b+c$?
Nov
26
comment Find sequence of differentiable functions $f_n$ on $\mathbb{R}$ that converge uniformly, but $f'_n$ converges only pointwise
Rotate the picture in this post by $\frac{\pi}{4}$ and take the top half of the picture to make them functions: math.stackexchange.com/questions/12906/is-value-of-pi-4
Nov
26
answered Prove Using Definition that the Sequence $\frac{n+1}{\sqrt{n}+2}$ Diverges to Infinity
Nov
23
comment Checking a possible proof of Fermat's Last Theorem
$$z^{2p} - 4(xy)^{p} = (x^p+y^p)^2- 4(xy)^{p}= (x^p-y^p)^2$$ so your $c=x^p-y^p$ ;)
Nov
23
answered Kernel of the deriative of a polynomial on $F[x]$
Nov
23
answered If $\gcd(a,b) = 1,$ then why is the set of invertible elements of $\mathbb Z_{ab}$ isomorphic to that of $\mathbb Z_a\times \mathbb Z_b$?
Nov
23
comment Why is $f(x) = x + \frac{1}{x}$ a mapping contraction?
@Stef For $x \neq y$ the inequality $d(f(x),f(y))\le Cd(x,y)$ for some $0 < C <1$ is equivalent to $d(f(x),f(y)) < Cd(x,y)$ for some $0 < C <1$... One implication is obvious, while the other can be obtained by making $C$ bigger.