1d
comment How to prove that the function $f(x)=0.1\,e^{-0.2|x|} $ is a probability density, and then use it?
Standard textbook shorthand for two questions... What proportion of errors are negative? What proportion of errors are at most 2?
1d
comment Symbol for unknown relation?
Go ahead and use a box if you want. Maybe you are trying to decide among $<$, $>$, and $=$, for example. Make sure your steps are reversible, and go for it.
1d
comment Does the class of all finite unions of closed-open intervals on $\mathbb{R}$ form a ring sets?
Yes, a bit confusing. When it says "all finite unions of" it is supposed to include in particular the union of zero of them.
1d
comment An Elliptic Integral - What's the Simplest Answer?
Whether you use $E(k)$ as Maple does, or $E(m)$ as Mathematica does, where $m=k^2$.
1d
comment Integral of a case function
And, more generally: an integral of a function defined in cases can be done by converting it to several integrals, one for each case. Here, all other cases are zero, so Harry left them out. A typical example of this is an integral involving absolute values.
1d
comment There is no smallest infinity in calculus?
For functions going to $+\infty$, just use $\log(f(x) \vee 1)$. It still goes to $+\infty$, and is slower.
1d
comment History of powers beyond squares and cubes
I read somewhere (maybe someone has a reference) that in the classical Greek geometry powers 4 and up never appear. Second power is area, third power is volume, and geometry is a theory to describe the real world, so higher powers are nonsense. Or something to that effect.
1d
comment Integral of $\exp(-x\,f(x))$
A famous example is the case $f(x)=x$. The indefinite integral $\int e^{-x^2}\,dx$ is not an elementary function.
1d
comment In primary school I was showed this. Why does it work?
Many of these problems, amazing to 5th graders, are easy to verify using algebra ... Maybe the next time one of them asks you why it works, tell them that. Maybe they will look forward to algebra (for a change).
1d
comment borel sigma algebra and closed rectangles
Believe it or not, instructors can help students when they are stuck on homework...
2d
comment borel sigma algebra and closed rectangles
It looks like you should consult your instructor for help on this.
2d
comment Errata database?
It's too bad this went away. You can still see it in web archives like the WayBack Machine. But the last update was 2007. A reason that errata lists should be in permanent places.
2d
comment There is no smallest infinity in calculus?
And the point is: "Is there a smallest infinity in calculus?" is not a nonsense post, by someone without a clue.
2d
answered There is no smallest infinity in calculus?
2d
comment borel sigma algebra and closed rectangles
Please tell us your thoughts and attempts. In (a), for the two sigma-algebras, can you show one is contained in the other?
2d
comment How would I graph a plot of this in Sage?
This appears to be a Sage question, and not a mathematics question.
Sep
16
comment Prove that $A$ is Lebesgue measurable implies that $x+A = \{ x+y : y \in A \}$ is measurable
Well, first prove $m^*(x+A) = m^*(A)$ for all sets $A$.
Sep
16
comment Prove that $A$ is Lebesgue measurable implies that $x+A = \{ x+y : y \in A \}$ is measurable
My answer is: yes prove it directly using the definition of Lebesgue measure. What is the definition of Lebesgue measure in that textbook?
Sep
16
comment Prove that $A$ is Lebesgue measurable implies that $x+A = \{ x+y : y \in A \}$ is measurable
But then he would have to show the translate of a null set is null. Probably no easier than the original problem.
Sep
16
comment Does $\pi$ encode the prime numbers?
No, of course not.
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