Ansgar Esztermann
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 Mar 11 comment Finding the basis of a vector space $\Bbb{W}$ Instead of starting with a family of vectors that might be a basis, try starting with a single vector, then look for a second, linearly independent, vector, and so on. See the link given by Umberto P. (it even contains a complete answer). Mar 11 comment Finding the basis of a vector space $\Bbb{W}$ What have you tried so far? Are there any particular points you have trouble with? Nov 13 comment Addition in linear vector spaces Addition of scalars is commutative even if much less than the full field axioms are given, e.g. in a quasi-field (multiplication neither commutative nor associative, only one distributive law), see math.stackexchange.com/questions/724122/…. Thus, to get non-commutative scalar addition, the requirements for the scalar structure would have to be relaxed considerably. Oct 16 comment Inverse image of a closed interval is compact @jlang: No, the preimage of [0,1] under $f$ is a subset of $D$. Oct 14 answered Prove that $S= \{ (x,y) : x^2 - y^2 <1 \}$ is open in $\mathbb{R}^2$ May 31 awarded Enthusiast Apr 25 comment If G is a finite abelian group and $a_1,…,a_n$ are all its elements, show that $x=a_1a_2a_3…a_n$must satisfy $x^2=e$. What you have defined is obviously not a group. E.g. you've already seen that 22=6=42, but then (22)3=(42)3 and -- if associativity would hold -- 2=4. Apr 24 answered 5 digit number $a6a41$ divisible by 9 Apr 11 answered Equivalence relation: prove that $(X \cap Y)$\ $E$ $\subset (X$ \ $E) \cap (Y$ \ $E)$ Apr 9 comment Equivalence relation: prove that $(X \cap Y)$\ $E$ $\subset (X$ \ $E) \cap (Y$ \ $E)$ Are you sure that you have written the inclusion in the right direction? Apr 9 comment How do I find arccos(-16.503) So, the problem seems to lie in an earlier step. How did you arrive at the expression $\arccos(-16.503)$? Apr 4 comment cartesian product $A^2 = A$, possible? Am I missing something, or should it be $A_\omega\times A_\omega\subset A_\omega$? Apr 3 awarded Yearling Apr 3 comment Limit definition by ordinal numbers Principia Mathematica, *207: "A term x is said to be the "upper limit" of alpha in P if alpha has no maximum and x is the sequent of alpha. In this case, x immediately follows the class alpha, though there is no one member of alpha with x immediately follows." Apr 3 answered How multiple of number is determined? Apr 2 comment Can two function $f$ and $g$ have same values through out a given interval and different values outside that interval? @user136561: This merely shows the difference (within a certain interval) is smaller than the resolution of the computer monitor. Apr 1 answered Show that for triangle ABC, with complex numbers for the coordinates, that we have the following equation Apr 1 comment Why does $f(x)=ax^2 + bx + c \ge 0\ \forall x \in \mathbb R$ imply $f$ has at most one real distinct root and discriminant $D \le 0$? @Sabyasachi: Take $a=1$, $b=c=0$. Mar 28 comment Show from the axioms: Addition in a quasifield is abelian @azimut: Thanks, I've added the answer accordingly, fixing an incorrect eq reference along the way. Mar 28 revised Show from the axioms: Addition in a quasifield is abelian Fix an incorrect reference; incorporate suggestions from comments