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Dec
19
answered List all degree one, two, three polynomials.
Dec
18
comment fair die or not, from 3D printer
Strictly speaking, the probability that your die is fair is zero, because even, say, a probability of $1/6+10^{-100}$ for getting a 6 would not be a fair die. If you want a non-zero probability, you need to specify acceptable deviations from the fair die.
Dec
16
comment What is the maximum number of $2$-inch by $2$-inch by $2$-inch cubes
Hint: If you build a cuboid out of $2"\times2"\times2"$ cubes, what property does the cuboid have?
Dec
16
revised Rewriting $\sin(\arccos(y))$ and $\arcsin(\cos(x))$
replaced image of formulas by MathJax formulas, other formatting and spelling corrections
Dec
16
revised Complex numbers getting too complex!
added 6 characters in body
Dec
16
revised Finding an invariant subspace of a linear operator.
edited title
Dec
15
answered 12 bit strings with more zeros than ones
Dec
14
comment Is $(-2)^{\sqrt{2}}$ a real number?
Actually there's no $k$ such that $\sin\left((2k+1)\sqrt{2}\pi\right)=0$ because $\sin x=0$ iff $x$ is an integer mutiple of $\pi$, and $(2k+1)\sqrt{2}$ is non-integer for any integer $k$. So there's no reason to restrict to the principal value; no possible value of $(-2)^{\sqrt{2}}$ is real.
Dec
14
comment Suppose that $R_1$ and $R_2$ are reflexive relations?
Suppose this post had a meaningful title.
Dec
14
comment What does $\frac{d^6y}{ dx^6}$ mean?
If the $\mathrm d$ in $\mathrm dx$ were considered an independent factor, you could just cancel it out in $\frac{\mathrm dy}{\mathrm dx}$ to obtain $\frac{y}{x}$. Which obviously is not a valid transformation.
Dec
13
revised Can sets have derivatives?
edited body
Dec
13
revised Can sets have derivatives?
Added something about extending the definition beyond just functions.
Dec
13
answered Can sets have derivatives?
Dec
13
comment Why must a topology on a set contain the empty set?
It's not necessary, just more convenient. Just as for intersections, you could just rewrite the requirement, in this case to "every nonempty family of open sets has an open union". That's not inconsistent, just more complicated.
Dec
12
comment Does “Doing a thing to both sides of an equation” have a name?
If you define "substitution" as "any replacement on one side that keeps the (in)equality true" then your point (1) reduces to "either we modify one side or both sides in a way that preserves the (in)equality", which obviously is true.
Dec
12
answered $f$ continuous on $(a,b)$ and $|f|$ differentiable on $(a,b)$; is $f$ differentiable in $(a,b)$?
Dec
12
comment $f$ continuous on $(a,b)$ and $|f|$ differentiable on $(a,b)$; is $f$ differentiable in $(a,b)$?
The function does not necessarily change its sign every time $f(x)=0$ (consider $f(x)=x^2$). Of course only those where it does may be "problematic"; it's just the "i.e." that is wrong.
Dec
9
awarded  Notable Question
Nov
1
answered Show the following is a group $a * b=a+b+ab$
Nov
1
answered Determine the complex function $f\left ( z \right )$