14,992 reputation
11940
bio website math.brown.edu/~lubinj
location Minnesota
age 78
visits member for 3 years, 2 months
seen 10 hours ago

Aged mathematician


Dec
10
comment Why it is not a function
I especially like your last paragraph: thank you.
Dec
9
awarded  Caucus
Dec
9
awarded  complex-numbers
Dec
8
answered Another way to prove that if n$^{th}$-degree polynomial $r(z)$ is zero at $n+1$ points in the plane, $r(z)\equiv 0$?
Dec
8
comment $f'(a)=0$ implies $x=a$ is not a simple zero of $f$
Not every useful fact has a Name.
Dec
8
comment Deriving the ultrametric from the p-adic norm?
I just got a confirmation. He finished his degree in 2001, and says he heard it out of Sally’s mouth as a sophomore at Chicago. That would put the remark at around ’94, I reckon. He says it looked unprepared, and that PS seemed surprised at the class’s reaction.
Dec
8
comment If the transformation is not onto, does that mean that it is not one to one?
It’s pretty clear from your use of the word “nullity” that you were thinking of $T$ as a linear transformation of a vector space $V$. You should have said this, and also specified whether $V$ was to be finite-dimensional or not.
Dec
7
comment What is the domain of continued fraction?
I think that OP meant that $i + \frac1i=0$. {The tail end of his c.f.)
Dec
7
comment Criteria to check for subfield and subdomain
My comment was for a field; to show $\mathbb Z[i]$ is a subdomain of $\mathbb C$, you have to show it’s closed under multiplication and subtraction; and that the multiplicative unity of $\mathbb C$ is in $\mathbb Z[i]$. And that’s all.
Dec
7
comment Deriving the ultrametric from the p-adic norm?
My student claims he heard Paul S say that (I think). I’ll confirm.
Dec
7
comment Criteria to check for subfield and subdomain
You need to check also that the multiplicative unit is in $S$, and that the reciprocal of every nonzero element of $S$ is in $S$. Think of $\mathbb Z\subset\mathbb Q$ as a counterexample.
Dec
7
comment Solving $\sqrt{2}\times\sqrt{15}$
What one wants to solve are equations only. Perhaps you want to simplify this, or express the product as the square root of a single number? If your teacher asked you to “solve” this, then (s)he was being very imprecise.
Dec
6
comment Deriving the ultrametric from the p-adic norm?
*A doctoral student of mine claims to have been in Paul’s class when he said that; and that he didn’t understand the laughter.
Dec
6
comment An Open Interval and a Half-open Interval are not Homeomorphic
By my lights, this is a complete proof.
Dec
6
comment Characteristic of a Ring not making sense.
No, not correct. $1_R$ added to itself $n$ times gives $0_R$. Adding $1_R$ to itself $n$ times does not give $n$ because $n$ is an integer (more exactly a natural number), and $n$ is not in the ring $R$ (unless of course $R$ contains $\mathbb Z$). And this really becomes interesting when $R$ doesn’t contain $\mathbb Z$.
Dec
5
answered Characteristic of a Ring not making sense.
Dec
5
answered What is the process of expanding quadratic equation
Dec
4
comment Basis of a field in a subfield
If $F\subset K$, any basis will be a subset of $K$, not $F$. Maybe you meant a basis for $K$ over $F$. It’s a fairly deep theorem that any vector space $V$ over the field $F$ has a basis, even if the basis is infinite. There’s nothing special about the vector space $K$, even though it’s also a field in its own right.
Dec
4
answered Composition of Inverse Functions
Dec
4
answered Find all irreducible monic polynomials of degree 3 in $\mathbb Z/3\mathbb Z[x].$