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Oct
10
comment On the proof that for $0<x<1$ there exists a real number $a$ s.t. $x^n < a$
Shouldn't the (independent of $n$) choice $a=1$ always work?
Oct
10
comment Definition of “simplify”
"I don't know if anyone's ever tried to define "simple" in any objective way," — computer algebra systems usually contain a simplify function; that certainly needs to use an objective metric. Of course the "simpler" expressions don't necessarily look simpler to the human looking at them (for example, Mathematica thinks that $(-1+x)^2$ is simpler than $(1-x)^2$).
Oct
9
comment Determine whether a function can be extended
What about the path $\alpha=\theta^m$? Then $\theta^m/\alpha = 1$ for every $\theta\ne 0$, and therefore the limit along this path is $1$ for $\theta\to 0$.
Oct
9
revised Determine whether a function can be extended
fixed MathJax formatting
Oct
9
revised Why does $\sqrt{2x+15}-6=x$ have an “imposter” solution?
added 26 characters in body
Oct
9
answered Why does $\sqrt{2x+15}-6=x$ have an “imposter” solution?
Oct
7
comment Prove, axiomatically that $1$ does not equal $0$.
@RobertSoupe: If $1=2$ then $1\times 2=1$ does not contradict $1\times 2=2$; indeed, you can derive $1\times 2=1$ from $1\times 2=2$ and $1=2$ (Just use the Euclidean relation property of equality).
Oct
6
comment Why is $f(x) \delta(x) = f(0)\delta(x)$ only true when $x=0$?
Well $\int f(3)\delta(3)\,\mathrm dx=0\ne f(0)$ in general. It's always the same: Plug it in the integral and look if it is (a) defined and (b) gives the same result. If the answer to both is yes, then the replacement is allowed, otherwise it isn't.
Oct
6
answered Why is $f(x) \delta(x) = f(0)\delta(x)$ only true when $x=0$?
Oct
6
comment Prove, axiomatically that $1$ does not equal $0$.
$1\times 2=1$ only contradicts $2\times1=2$ if $1\ne 2$.
Oct
5
comment How to prove the set G is a group with operation *
Since $\sigma_a$ is surjective, there exists a $g_a$ so that $\sigma_a(g_a)=a$. Similarly, since for every $b$, $\phi_b$ is surjective, there's always a $h_b$ so that $\phi_b(h_b)=b$.
Oct
4
comment Is zero the center of the numeric sequence?
Unlile $x\mapsto -x$, both $x\mapsto n-x$ and $x\mapsto n+x$ don't preserve the additive structure of the number line. Distance is not the only thing symmetry can preserve.
Oct
4
comment Why do differentiation rules work? What's the intuition behind them? (Not asking for proofs)
What is FOIL? I've never encountered that acronym (I assume it is one, as it's all uppercase).
Oct
3
revised $\mathbb{R}$ is not contained in $\mathbb{C}$
added clarification suggested by Asaf Karagila
Oct
3
comment $\mathbb{R}$ is not contained in $\mathbb{C}$
@AsafKaragila: You're right, it's better to explicitly spell it out. I'll edit my answer accordingly.
Oct
3
answered $\mathbb{R}$ is not contained in $\mathbb{C}$
Oct
3
comment Set theory possible values
With the given information, you won't be able to give a precise value. Just like you cannot give a precise value for my height if I tell you I'm less tall than Abraham Lincoln.
Oct
3
comment Show $\{\emptyset,\{0,1,2\},\{0\},\{1,2\}\}$ a topology on the set $\{0,1,2\}$?
So where is your problem in calculating the unions and intersections of the sets in $\tau$?
Oct
3
accepted Basis for series that converge for all complex numbers?
Oct
3
comment Set theory possible values
"Any number smaller than $0.7$" would also include values like $-1$. On the other hand, it would exclude $0.7$ itself, which is possible if $C\subseteq A\cup B$.