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May
11
comment Does finite expectation imply bounded random variable?
@mathse measure zero doesn't count ("$|X|<\infty$ a.s.")
May
10
answered An infinite non-Abelian group with an involutive automorphism that preserves only the identity?
May
10
comment Conjecture: Only one Fibonacci number is the sum of two cubes
$F_{3n}-F_{n+1}^3$ is relatively small and hence has some chance to be a cube "by chance". But otherwise the exponential growth makes the existence of larger solutions somewhat unlikely.
May
10
comment Question about the non-hausdorffness of the cofinite topology
To stress what egreg said: If $X$ is finite then the cofinite topology is the discrete topology an dhence Hausdorff. So the condition that $X$ is infinite is missing from th eproblem statement!
May
10
answered What is the minimum value of $abc$
May
10
comment What is the minimum value of $abc$
My bet: $a,b,c$ must be nonnegative integers and double root is not allowed.
May
10
comment What is the minimum value of $abc$
@Samurai I have given an explcit example with $abc=\frac5{36}$ already in my previous comment. Did you perhaps forget an important condition on $a,b,c$ (such as: nonnegative integer)?
May
10
comment What is the minimum value of $abc$
@boxed__l We cannot take $k=\pm\infty$, only consider $k\to\pm\infty$; whatever $M\in\mathbb R$ you pick, one can pick $k$ with $|k|$ large enough to ensure $k^3abc<M$. Strictly speaking, $-\infty$ is not make the minimum, but the infimum of all possible $abc$. Also, we need to ensure that there exists such a polynomial with $abc\ne0$ in the first place. $(x-\frac12)(x-\frac13)=x^2-\frac56x+\frac16$ shows this.
May
10
answered Find the sum of $\displaystyle\sum_{i=0}^k \dbinom{n+i}{i}$
May
10
comment Is a complex number whose real and imaginary parts are both transcendental transcendental?
For the second question, if $z=a+bi$ is algebraic and $b$ is algebraic, then $a=z-i\cdot b$ is also algebraic.
May
10
answered Area of a square inscribed in a triangle?
May
10
answered Why the discriminant determine whether a quadratic has real roots or not?
May
10
answered Last 3 digits of $3^{999}$
May
10
comment decimal representation of $2^m$ starts with a particular finite sequence of decimal digits
.. with $a_1\ne 0$?
May
10
comment Can we define the equality as $a=b$ iff $\frac{a}{b}=1$?
How do you define $\frac ab{\color{red}=} 1$ then?
May
10
comment Why is $\phi$ an epimorphism of rings?
If each element of some set is of the form "something of $a$" where $a$ is from some other set, then the map "take something of ..." is clearly a surjective map from that other set to the given set. - if $A=\{\,f(x)\mid x\in B\,\}$ then $f\colon B\to A$, $x\mapsto f(x)$ is clearly onto.
May
10
comment Security of permutation function
Well, yes, by nomenclature this is a permutation of the bits.
May
10
comment Showing that $\cos(z)$ has an essential singularity at $\infty$
Alternatively, assume that $\cos z$ has a pole of order $k\in\mathbb Z$ at $\infty$. Then $f(z)=z^k\cos\frac1z$ has the properties $f(0)\ne 0$ and yet a sequence of zeroes converging to $0$ ...
May
10
answered Proving a metric with absolute value
May
10
comment Proving a metric with absolute value
Monotonically increasing is not enough. $x\mapsto x^2$ is also monotonically increasing for $x\ge 0$, and yet $|x-y|^2$ is not a metric.