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Jul
28
revised Unit circle is divided into $n$ equal pieces, what is the least value of the perimeters of the $n$ parts?
added 205 characters in body
Jul
28
revised Unit circle is divided into $n$ equal pieces, what is the least value of the perimeters of the $n$ parts?
added 205 characters in body
Jul
28
answered Unit circle is divided into $n$ equal pieces, what is the least value of the perimeters of the $n$ parts?
Jul
28
comment Tangent line at $x_1$ to polynomial curve $p(x)$ of degree at least $2$ implies $x_1$ is a double root of $p(x) - p^{'}(x_1)(x-x_1)$?
@user111854 if $h(x)=(x-x_0)^kh_1(x)$ with some polynomial $h_1$, then $h'(x)=k(x-x_0)^{k-1}h_1(x)+(x-x_0)^kh_1'(x)=(x-x_0)^{k-1}h_2(x)$ with $h_2(x):=kh_1(x)+(x-x_0)h_1'(x)$, i.e. each higher derivative has one factor $(x-x_0)$ less.
Jul
28
answered Tangent line at $x_1$ to polynomial curve $p(x)$ of degree at least $2$ implies $x_1$ is a double root of $p(x) - p^{'}(x_1)(x-x_1)$?
Jul
25
comment RSA encryption. Breaking 2048 keys with index
In other words, the key to breaking the randomly generated keys is to convince people to use your specialized random number generator :)
Jul
23
comment Paradoxical Game Show Problem
As soon as you impose a probability distribution on the money amounts, the paradox gets resolved (because when seeing an unusually high amount in your chosen box, the probability that yours is the smaller amount decreases)
Jul
23
revised finding a group that satisfy: $x,y\in A_n\Rightarrow x\in y \vee y\in x \vee y=x$
edited tags
Jul
23
comment finding a group that satisfy: $x,y\in A_n\Rightarrow x\in y \vee y\in x \vee y=x$
What about the set $n$ itself?
Jul
23
answered Equivalence Graphs
Jul
23
comment My proof of the recursion principle (without the axiom of replacement)
I'm not very happy with "maximum element of domain". Why not use replacement to take the domain of $f$ itself? (This may require some special cases near $0$) Or do you already have $n^-$ on $\mathbb N\setminus\{0\}$ readily available?
Jul
23
comment Prove that intersection of connected spaces is connceted.
Let $A$ be the unit circle and $B$ the $x$-axis within the two-dimensional plane. Which of $A,B,A\cap B$ are conncted?
Jul
23
comment Why does this graph only the positive side
Hint: Do you think that $\sqrt[4]{x^2}=x^{2/4}=x^{1/2}=\sqrt x$ for all real numbers $x$?
Jul
23
answered Question concerning how a map extends to a homomorphism.
Jul
22
comment Where's the problem with a false “proof”: $\;1^0 = 1^2 \overset{?}\implies 0 = 2$
Apparently it is. Otherwise, we'd have $0=2$.
Jul
22
comment Does the boundaries of non-disjoint sets in Euclidean space have common element?
Well, you need to add a few conditions. For example if the sets are open, not disjoint, not contained in one another, and connected ...
Jul
22
comment Primitive-recursive functions and polynomial equations
Unless $K(m,n)$ is constant, $\prod_{i=0}^{K(n,m)}(P(n,m,i)-Q(n,m,i))$ is not of the form $P(n,m)-Q(n,m)=0$.
Jul
22
answered Primitive-recursive functions and polynomial equations
Jul
22
comment Proving some properties of $\Bbb N$ without using recursion
@Graduate I don't think that William wanted to object against referencing the axioms, but against referencing them by a local obscure notation. Saying Axiom of Infinity or simply INF instead of ZF7, Axiom of Power Set or simply POW instead of ZF4, Axiom Schema of Separation or simply SEP instead of ZF5 would have made a reference to the axioms as intended - and the reader would know which are meant.
Jul
22
answered Proving some properties of $\Bbb N$ without using recursion