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1d
comment The space $C[0,1]$ with the metric defined by $d(f,g)=\int _0^1|f(t)-g(t)|dt$?
Stone Weierstrass theorem.
1d
revised Computing $C_0^2+C_1^2+C_2^2+C_3^2+ \cdots +C_n^2$
Removed unnecessary cdots
1d
suggested suggested edit on Computing $C_0^2+C_1^2+C_2^2+C_3^2+ \cdots +C_n^2$
1d
answered $ (3+\sqrt{5})^n+(3-\sqrt{5})^n\equiv\; 0 \; [2^n] $
Oct
29
comment Proving entire function is constant
You can check it is constant using the CR equations. The exponential function is not real valued, it is not true that $\exp(z)\in \Bbb R$ for all $z\in \Bbb C$.
Oct
29
comment Proving entire function is constant
$f+\overline f$ is bounded because is constant. If $f=u+iv$, then $f+\overline f=2u\in \Bbb R$, but a holomorphic real valued function must be constant.
Oct
29
comment Proving entire function is constant
$\overline{\sin(z)}$ is not entire. We are just using the hypothesis to show $f(z)+\overline f(z)$ is entire on $\Bbb C\setminus \{0\}$.
Oct
29
answered Proving entire function is constant
Oct
26
comment The primes such that removing digits from the right end leaves another prime
en.wikipedia.org/wiki/Truncatable_prime
Oct
26
comment Image of a square modulo
homepages.math.uic.edu/~leon/mcs425-s08/handouts/…
Oct
23
comment How do I prove that this is or isn't isomorphic?
For example here.
Oct
23
comment How do I prove that this is or isn't isomorphic?
In general, $\mathbb Z_m\times \Bbb Z_n \cong \Bbb Z_{mn}$ iff $(m,n)=1$. I'm sure this has been asked many times here before.
Oct
13
comment Prove sequence converges
See here: Convergence infinite product.
Oct
12
comment What is the dimension for this subspace?
From $x-y-z=0$, you get $z=x-y$. Hence, using the first equation, $0=x+y+z=x+y+(x-y)=2x$, which means $x=0$. Both equations reduce to $y=-z$. Then any vector in $S$ must be of the form $\lambda(0,-1,1)$.
Oct
9
revised Continuous on an interval implies continuous on every subinterval?
Edited tags
Oct
9
suggested suggested edit on Continuous on an interval implies continuous on every subinterval?
Oct
9
comment Continuity Question in Analysis
Hint: Use the definition of continuity at $a$ with $\varepsilon=\dfrac{f(a)}{2}$.
Oct
7
comment What does $ \sum_{i = 1}^{\infty} \frac{1}{i(i-1)!}$ converge to?
Hint 2: Exp...${}$
Oct
6
comment $f(x)=\frac{x}{1-|x|}$ is not uniformly continuous
Not necessarily. The image of $f$ would be bounded if, for instance, its domain were compact.
Oct
6
comment $f(x)=\frac{x}{1-|x|}$ is not uniformly continuous
$f$ is continuous.