10,281 reputation
930
bio website danshved.wordpress.com
location Moscow, Russia
age 28
visits member for 1 year, 11 months
seen 10 hours ago

I'm a graduate student at MIPT, Russia. My thesis is in the theory of groups, but I like lots of other things too )


12h
comment What are all different (non-isomorphic) field structures on $\mathbb R \times \mathbb R$
@AsafKaragila I don't see how Hayden is beeing too literal. His answer clearly shows that at least two field structures are possible: one isomorphic to $\mathbb{R}$, the other to $\mathbb{C}$.
12h
comment What are all different (non-isomorphic) field structures on $\mathbb R \times \mathbb R$
What you're asking is to list all the fields with cardinality $2^{\aleph_0}$. There are lots of those.
14h
comment Is there any easy way to see that elementary matrices commute in $\text {Mat}_{n \times n} (\mathbb F)$?
Another argument why this isn't so. Each nondegenerate matrix is a product of elementary matrices. If elementary matrices commuted, all nondegenerate matrices would commute! This would be way too good to be true.
2d
comment Prove that $e^x \ge$ its Maclaurin polynomial with n terms
Did you mean $x \geq 0, n \in \mathbb{N}$ in (c)? It looks weird otherwise.
Oct
18
revised A boy's father is 25 years older than him. The sum of their ages is 31. How old is the boy?
added 2 characters in body
Oct
18
comment $\mathbb R[x]/\langle x^2+1\rangle$ is a field
@mcmat23 you probably mean that every non-zero prime ideal is maximal :-)
Oct
18
answered $\mathbb R[x]/\langle x^2+1\rangle$ is a field
Oct
18
revised A boy's father is 25 years older than him. The sum of their ages is 31. How old is the boy?
added 1 character in body
Oct
18
revised A boy's father is 25 years older than him. The sum of their ages is 31. How old is the boy?
added 394 characters in body
Oct
18
answered A boy's father is 25 years older than him. The sum of their ages is 31. How old is the boy?
Oct
18
revised If a is not relatively prime to n prove modulo property
added 282 characters in body
Oct
18
answered If a is not relatively prime to n prove modulo property
Oct
18
answered Let K be field and L be a subfield prove that
Oct
18
answered Proving ring $R$ with unity is commutative if $(xy)^2 = x^2y^2$
Oct
18
comment Does $1.0000000000\cdots 1$ with an infinite number of $0$ in it exist?
@user1485853 It's hard to find a satisfying answer, probably because your phrasing is very vague and unclear. Nevertheless, let me make two notes. First: nowadays, something being "ridiculous" is never used as an argument in a mathematical text. Or, if it is, then only as shorthand for something very precise. Second, consider this: people distinguish between sequences that converge to $\infty$, to $+\infty$, and to $-\infty$. This already looks like three distinct "infinities" to me, and one can encounter all of them in an ordinary Calculus class.
Oct
18
comment Does $1.0000000000\cdots 1$ with an infinite number of $0$ in it exist?
@user1485853 No, I never said that. What I said is that decimal representations are by definition restricted to sequences indexed by natural numbers. It means that in a decimal representation of a number every digit is preceded only by a finite number of digits, which renders the OP's construction "illegal" (i.e. whatever it is, it is not a decimal representation, as already mentioned by André Nicolas).
Oct
18
awarded  Pundit
Oct
18
comment Are matroids really a generalization of independence in vector spaces?
On second thought, there's no need to require that the set isn't contained in $\{0\}$. Any finite subset of a vector space is a matroid.
Oct
18
comment Is HHH a congurence criteria for triangles?
Don't know what SSS is, but this is clearly the correct answer :)
Oct
18
comment Are matroids really a generalization of independence in vector spaces?
No, not every matroid is represented by some vectors of a linear space. Not every matroid is linear. But the converse holds: any finite subset of a vector space not contained in $\{0\}$ is a matroid (w.r.t. linear independence).