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Nov
19
answered Does $\langle(4,4,4),(1,2,2)\rangle=\langle(1,2,1),(1,0,1)\rangle$?
Nov
19
comment Does $\langle(4,4,4),(1,2,2)\rangle=\langle(1,2,1),(1,0,1)\rangle$?
\langle is $\langle$, and \rangle is $\rangle$.
Nov
19
revised Does $\langle(4,4,4),(1,2,2)\rangle=\langle(1,2,1),(1,0,1)\rangle$?
Better LaTeX.
Nov
19
comment Is there anything wrong with this use of the axiom of choice?
@Andreas: Good point; I was sloppy. Better now?
Nov
19
revised Is there anything wrong with this use of the axiom of choice?
added 136 characters in body
Nov
19
answered Rings whose elements are partitioned between units and zero-divisors.
Nov
19
comment Let $G$ be an abelian group. Show that the mapping $\phi:G\to G$ given by $\phi(x) = x^{-1}$ is an automorphism of $G$.
@Arnold: Same idea: if $G$ is not Abelian, then there are $x,y\in G$ such that $xy\ne yx$. Now consider $\varphi(x^{-1}y^{-1})$.
Nov
19
answered Let $G$ be an abelian group. Show that the mapping $\phi:G\to G$ given by $\phi(x) = x^{-1}$ is an automorphism of $G$.
Nov
19
revised Let $G$ be an abelian group. Show that the mapping $\phi:G\to G$ given by $\phi(x) = x^{-1}$ is an automorphism of $G$.
LaTeX.
Nov
19
revised Let $m$ and $n$ be integers in the ring of integers. Show that if $m\mathbb Z$ contains $n\mathbb Z$ if and only if $m$ divides $n$
edited tags
Nov
19
answered Is there anything wrong with this use of the axiom of choice?
Nov
19
answered Trying to understand matrix image
Nov
19
answered Longest increasing subsequence
Nov
19
answered Prove that if $A \setminus B = \emptyset$, then $A \subseteq B$
Nov
19
answered Counting Problems.
Nov
19
comment Prove that set of all lines in the plane is uncountable.
@Koba: Right, and each line containing two or more rational points is determined by two of those rational points, so there are only ...
Nov
19
awarded  divisibility
Nov
19
answered isomorphisms- subspaces in topology
Nov
19
comment Prove that set of all lines in the plane is uncountable.
@user99680: One of the two types named in the question.
Nov
19
comment Prove that set of all lines in the plane is uncountable.
Certainly infinitely many, but what kind of infinite?