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visits member for 2 years, 11 months
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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
20
comment ZFC, NBG and Naive set theory
@AndresCaicedo: I stand corrected. If you submit an answer of your own, I'll retract mine.
Oct
17
answered ZFC, NBG and Naive set theory
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