12,454 reputation
11332
bio website math.brown.edu/~lubinj
location Minnesota
age 77
visits member for 2 years, 9 months
seen 9 hours ago

Aged mathematician


9h
comment How to solve for $x$ for $\frac{1}2 x^{-1/2}- \frac14x^{-3/4}$
Strictly speaking, it’s only an equation that may be solved for one of the variables. Without an equals sign, it’s not automatically clear what you’re asking for. In fact, I assumed that you had $y$ equaling the expression you wrote, and wanted to solve that for $x$ (in terms of $y$).
1d
comment $\Bbb Z^\ast$ What is this notation?
For an algebraist, $\mathbb Z^*$ would certainly be the set of invertible elements in the multiplicative monoid, i.e. $\{\pm1\}$, but that interpretation seems excluded by the context. Perhaps the notation is peculiar to the Brazilian educational system.
1d
comment How are $\pi/4$ and $3\pi/4$ solutions to $\sec^2 \theta -2 = 0$?
It certainly isn’t true that $\sec\theta$ never equals $2$. Indeed, that’s the same as cosine equaling $1/2$, which you know all about.
1d
comment Polynomial division problem
In other words, add up all the even-degree coeffs and you get the constant term; add up all the odd-deg coeffs and you get the linear term.
2d
comment Mistake in a question in Fulton's algebraic curves book?
Just by substitution. Can’t you express every polynomial in the $X$s as, instead, a polynomial in the $Y$s? And vice versa?
2d
comment Intuition behind topological spaces
Just because every neighborhood of $0$, and in particular each neighborhood $\langle-\varepsilon,\varepsilon\rangle$ has nonempty intersection with that open set.
2d
comment Fibonacci number that ends with 2014 zeros?
All of this must be known to Fib specialists, but that term doesn’t apply to me. By a cumbersome $p$-adic computation ($p=2,5$), I seem to have shown that for $m\ge3$, $2^m|F_k$ if and only if $3\cdot2^{m-2}|k$. And that $5^m|F_k$ if and only if $5^m|k$. This would show that your $750$, etc. are the smallest numbers satisfying the desired conditions.
Jul
19
comment Thinking of sohcahtoa with 90 in a triangle.
Of course the sine and cosine of a right angle can’t be defined using sohcahtoa, but one you believe the laws of sines and cosines, this is the best way.
Jul
18
comment x≡1 (mod 8) x≡9 (mod 12) has solution x = x_0. How many solutions mod 24 are there to the system of congruences?
It is easy: you look at all the numbers from $0$ to $23$ inclusive, and see which of them satisfy the given conditions. That’s pretty much it.
Jul
17
comment Inverted Circle?
I like your second formulation because it allows quick and easy hand computation of loads of rational points.
Jul
16
comment The $i^{th}$ prime in a given ring R
In spite of what both @PatrickDaSilva and I have said, I think the rings that come closest to your ideal are the rings of integers in quadratic imaginary fields which are unique factorization domains. Unfortunately, there are only finitely many of these. But as for $\mathbb Z[i]$, which is more or less typical, you at least have only at most two primes dividing each ordinary prime, and you can, again in spite of what we said, make a reasonable choice between each one of them and between the prime and it times a unit (which is usually just $\pm1$).
Jul
12
comment $E \subset \mathbb R$ is an Interval $\iff E$ Is connected
It seems to me that the text’s proof is not completely right. Disconnectedness of $E$ means that there are disjoint open subsets of $E$ with the specified property. So there would be open subsets $A$ and $B$ of $\mathbb R$ with $A\cap B\cap E=\emptyset$, not merely $A\cap B=\emptyset$.
Jul
12
comment Functions $f$ such that $f(x)+f(-x)=f(x)f(-x)$
Neat, very neat.
Jul
11
comment Completion of Complex Numbers
This answer seems very satisfying, to me.
Jul
11
comment Real Analysis: Showing $f: \Bbb Q \to \Bbb Q$ is continuous
For the case that $U$ contains $1$ but not $-1$, isn’t $-2$ in $f^{-1}(U)$?
Jul
10
comment What is the meaning of “fix” in field theory?
It’s not a specially mathematical term. One speaks of the “fixed stars” (as opposed to the planets): they don’t move. Or one can say “I am fixed in my opinion” to indicate that the opinion hasn’t changed.
Jul
10
comment names in a quadratic field extension
As an old-fashioned guy, I rebel against the use of “abscissa” and “ordinate”; I would use the terms first and second coordinates, or first and second entries, thinking of an $n$-tuple of things in the base as column matrices.
Jul
10
comment Triangle problem - finding the angle
Yes, but what method did you use for computing that algebraic number? Was it just a repeated application of Law of Cosines, or something else?
Jul
10
comment Triangle problem - finding the angle
You didn’t say how you got your sextic equation in cosine, did you?
Jul
10
comment Triangle problem - finding the angle
Yes, you seem to have used the Cubic Formula, which I have never been comfortable with.