Ansgar Esztermann
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 Mar11 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). Mar11 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? Nov13 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. Oct20 comment ZFC, NBG and Naive set theory @AndresCaicedo: I stand corrected. If you submit an answer of your own, I'll retract mine. Oct17 answered ZFC, NBG and Naive set theory Oct16 comment Inverse image of a closed interval is compact @jlang: No, the preimage of [0,1] under $f$ is a subset of $D$. Oct14 answered Prove that $S= \{ (x,y) : x^2 - y^2 <1 \}$ is open in $\mathbb{R}^2$ May31 awarded Enthusiast Apr25 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. Apr24 answered 5 digit number $a6a41$ divisible by 9 Apr11 answered Equivalence relation: prove that $(X \cap Y)$\ $E$ $\subset (X$ \ $E) \cap (Y$ \ $E)$ Apr9 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? Apr9 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 $\arccos(-16.503)$? Apr4 comment cartesian product $A^2 = A$, possible? Am I missing something, or should it be $A_\omega\times A_\omega\subset A_\omega$? Apr3 awarded Yearling Apr3 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." Apr3 answered How multiple of number is determined? Apr2 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. Apr1 answered Show that for triangle ABC, with complex numbers for the coordinates, that we have the following equation Apr1 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 $a=1$, $b=c=0$.