12,284 reputation
11332
bio website math.brown.edu/~lubinj
location Minnesota
age 77
visits member for 2 years, 9 months
seen 1 hour ago

Aged mathematician


Jan
3
answered How many times the parabola $y=x^2$ intersects the origin?
Jan
3
comment How many times the parabola $y=x^2$ intersects the origin?
You’re confusing the multiplicity of intersection of two curves (the parabola and the $x$-axis, for example) with the possibility that a single point might have greater multiplicity than $1$ on some curve. The origin is a simple point of the parabola, but the axis and the parabola do indeed have an intersection of multiplicity two there.
Jan
3
comment Geometric Proof that $\mathbb{Z}[\sqrt{-3}]$ is non-Euclidean
Euclideanness is not a geometric property, I would say. After all, polynomials over a field form a Euclidean domain.
Jan
2
comment Rational Root theorem issue
Well, you may have heard of the Cubic Formula. But NEVER teach this to high-school students.
Jan
2
answered Complex roots of the polynomial $bz^{2}+2az+b$ are on the unit circle
Jan
2
comment Rational Root theorem issue
Did you just make this example up on your own? If so, and you didn’t get it from a source, then the chances are that it has no roots and is irreducible. You can exclude all positive possibilities, as well as $-1$, because that sum is odd. You can exclude $-4$ because that sum is congruent to $4$ modulo $8$. Looks as if the other possibilities are no good either.
Dec
31
comment $\operatorname{Gal}({\mathbb Q(i,\sqrt[4]{2})}/{\mathbb Q})$
You show that it’s the dihedral group simply by writing down all the elements of the group (each determined by what it does to $i$ and the fourth root of $2$), and seeing how they compose. Don’t quail at the prospect: it’s a great exercise.
Dec
31
comment If real number x and y satisfy $(x+5)^2 +(y-12)^2=14^2$ then find the minimum value of $x^2 +y^2$
Looks to me like the high-school problem of drawing the smaller of the two circles through the origin that are tangent to the given circle.
Dec
30
answered Periodic automorphism of $S^{3}$ and fixed point set
Dec
30
comment Is cantor set homeomorphic to the unit interval?
In fact, Cantor is totally disconnected: its only connected subsets are singletons.
Dec
30
comment Find general term of a sequence
I would have simply written the first few terms and noticed that they all were of the form $(3^n-1)/2$. At this point, an inductive proof should be easy.
Dec
30
comment Cauchy product of series
Have you taken two convergent series of positive terms and multiplied them together? I mean by hand, just the first few terms? If not, I suggest that you try it and see what’s going on. There’s nothing mysterious about the “Cauchy product”, when you’ve done a little computation, it looks like the most natural thing in the world.
Dec
30
comment Writing ${{5-5\cdot x}\over{x}}+8\over{{1-x}\over{x}} + 1$ in one fraction
A formula is not necessarily a recipe. There’s nothing wrong with the method sketched by @Listing, but @okarin’s method here will almost always be faster. Remember that top and bottom of a fraction may always be multiplied by the same nonzero quantity, and the fraction’s value will be unchanged. Here, the magic nonzero quantity is simply $x$, but in other cases you may have to look just a little deeper.
Dec
30
comment Proving $f = x^8+x^7+x^3+x+1$ to be irreducible over $\mathbf{F}_2$.
There’s no problem with irreducible cubic factors, is there? If such a polynomial divided $f$, then its root $\rho$ (a primitive seventh root of unity) would be a root of $f$. But then $\rho^8+\rho^7+\rho+1=0$, and $f(\rho)=\rho^3\ne0$.
Dec
29
comment Modulo over rational numbers?
@user44197, yes, but I think that OP is interested in working modulo integral multiples of a nonintegral rational. I still think that anyone wishing to do so must do his own work of making the definition and notation explicit.
Dec
29
comment Modulo over rational numbers?
@BillDubuque, I say, Ah, but gdc and lcm are purely multiplicative gadgets, living in the free $\mathbb Z$-module with basis the primes. No addition involved whatsoever.
Dec
29
comment Modulo over rational numbers?
From my standpoint, this seems unusual and unorthodox enough that I’d recommend that the individual writer make her/his own definitions. Do you have a use for this?
Dec
27
answered Circumference of a circle in hyperbolic space
Dec
27
answered If $\Omega = \{1,2,3,\ldots,\}$, then $S_{\Omega}$ is an infinite group.
Dec
27
comment How do I put in words that $2\cos^2 x +\sin x-1$ cannot be factored?
I think that it’s really not clear what it means to factor an expression like this. I also think that it’s not legit to forbid yourself the (true) identity $\sin^2+\cos^2=1$, because without it, you’re not talking about the sine and the cosine at all.