Erland's latest activity

The three classical geometry problems: Doubling the cube, Trisecting the angle, and Squaring the circle, have no solutions. The proofs...

Yes of course. Thank you and sorry for the mistake!

Typo, I think: meant to say ##g(x)=f(x+a)-f(x)##.

Actually, a stronger result than your original can be proved. The Borsuk-Ulam Theorem says that if ##f: S^n\to \Bbb R^n## (where ##S^n##...

So, let us look at two specific examples and use pasmith's method: Example 1. $$y''-5y'+6y=0$$ The characterstic equation...

How does Bloch define ##\le## for natural numbers? I noticed that he used his theorem to prove ##1\le n## for all ##n \in \Bbb N##, but...

You can also view it this way: ##3\times 2=6## ##3.1\times 2.7=8.37## ##3.14\times 2.71=8.5094## ##3.141\times 2.718=8.527238##...

For this to work, the functions defined by the power series must be continuous at ##0##, as you pointed out in a later post. This...

We can also view it this way: 1. ##A\rightarrow B##. (Hypothesis) 2. ##A##. (Hypothesis) 3. ##B##. (1, 2: Modus ponens) 4. ##\neg A...

Here's a neat alternative that includes an idea that can be very useful. Imagine that whatever happens we always play at least 6...

It is not clear to me what the OP means by "taking random points that corresponds to hyperreal numbers on the hyperreal line". In the...

Smallest infinitesimal?? There is no such thing. More precisely, there is no smallest positive infinitesimal. If there was one, say...

I think the simplest way to do this is to prove that an affine transformation (linear tranformation + translation) changes the measure...

It's somewhat unclear to me what you mean by "pulling back". A real or complex valued function on a product space is measurable (w.r.t...

You are on the right track, I think. The product ##\sigma##-algebra in ##\Bbb R^2## generated by measurable rectangles (that is...