11,114 reputation
11230
bio website math.brown.edu/~lubinj
location Minnesota
age 77
visits member for 2 years, 6 months
seen 19 hours ago

Aged mathematician


1d
comment What sort of algebra is this?
I’d feel more comfortable if you had come across such things in the real mathematical world. Good luck!
1d
comment What sort of algebra is this?
Do you have a situation where this sort of thing arises?
2d
comment What is wrong with this, Calculator says OK, Homework doesn't
Looks perfectly right to me, unless the intent was $3/(5/3)$. Is it clear in the statement which of the two readings was desired? Only other thing I can think of is that the instructor was being overly fussy somehow.
2d
answered To find the distance of a point from ellipse
2d
comment Express $a^5$ in terms of $c_0+c_1a+c_2a^2.$
It’s evident that OP didn’t yet understand that the characteristic is inherited by the extension rings.
2d
comment Express $a^5$ in terms of $c_0+c_1a+c_2a^2.$
Very roughly speaking, any identity that occurs in the base field carries over to its extensions. But that statement is much too rough to hang your hat on!
2d
comment Express $a^5$ in terms of $c_0+c_1a+c_2a^2.$
$a^2\notin\mathbb Z/(2)$, but the characteristic is a property shared by all the fields that contain $\mathbb Z/(2)$. After all, since $-1=1$ in $\mathbb Z/(2)$, it then follows that $-z=z$ in any old ring containing $\mathbb Z/(2)$.
2d
comment How to Simplify Sin/tan problem.
Then it’s just a matter of doing that substitution and simplifying the complicated fraction.
2d
comment How to Simplify Sin/tan problem.
You’re aware that $\tan=\sin/\cos$?
2d
comment Express $a^5$ in terms of $c_0+c_1a+c_2a^2.$
Well, in characteristic two, plus is minus.
Apr
17
comment Common perpendicular
Just so. As you say, a pair of Type1 lines have no shortest distance between them, as I hope you’ve seen.
Apr
17
answered Methods for finding Number of roots in $\mathbb{Q}_{p}$ for a polynomial
Apr
17
answered Common perpendicular
Apr
17
comment Common perpendicular
A plausibility argument, not a proof: two such lines (they are geodesics, not horocycles) get close and closer as you go upwards, “meeting” at $i\infty$, with angle zero. If there were a common perpendicular, you’d have a “triangle” with sum of the angles equal to $\pi$, and thus with area zero.
Apr
17
comment Open Ball under the p-adic Norm
There are many cases when the Julia set of a polynomial acting on $\mathbb C$ is totally disconnected and looks exactly like $\mathbb Z_p$, which is the closed ball in $\mathbb Q_p$ of radius $1$, centered at $0$ (and the open ball of radius $1+\varepsilon$ for small enough $\varepsilon$).
Apr
16
revised General methods for solving p-adic inequality $|a^2+b|_{p}<p^{-k}$ for $a\in \mathbb{Z}$
clarification
Apr
16
answered General methods for solving p-adic inequality $|a^2+b|_{p}<p^{-k}$ for $a\in \mathbb{Z}$
Apr
15
comment Roots of polynomial in $F_3[x]$
$\alpha^2=-\alpha+1$ and $\alpha^4=-1$; neither of these is a root of $X^3+X+1$.
Apr
15
comment Finding the value of trigonometric functions
The important thing, beyond @Seth’s suggestion, is to remember that in view of the periodicity of $\tan$ and $cos$, you can add or subtract multiples of $\pi$ from the argument of $\tan$ without changing the value, similarly, you can add or subtract multiples of $2\pi$ from the argument of $\cos$.
Apr
15
comment Is the reasoning/algebra for my proof correct? (musical tuning theory proof)
That would have been my proof, but you got there first! (I would have pointed out that @SanathDevalpurkar’s proof was perfectly fine, but that this argument is much more basic.)