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Apr
13
answered Every set with more than point admits a permutation with no fixed point and the Axiom of Choice
Apr
13
comment Showing that an operator is the projection
1-codimensional subspace. As $L \ne 0$ (from $w \ne 0$), we have $L(w) = w$, We will show that $V = \ker(L) + span(w)$. Let $v \in V$, then $v = v - L(v) + L(v)$, with $(v - L(v)) \in \ker(L)$, $L(v) \in span(w)$. Hence $\ker(L)$ is 1-codimensional
Apr
13
comment Showing that an operator is the projection
Sry. Had an error in writing, I intended to write $w^\bot \subseteq \ker(L)$, as you state ... now use, that both are hyperolanes ...
Apr
13
revised Showing that an operator is the projection
added 24 characters in body
Apr
13
answered Showing that an operator is the projection
Apr
13
comment Diffeomorphism between a sphere and ellipsoid in $\mathbb R^3$.
$f^{-1}(x) = (ax_1, bx_2, cx_3)$?!
Apr
13
awarded  Steward
Apr
13
answered If $F$ is continuous and $\lim_{\left\|x\right\|\to\infty}F(x)=\infty$, then all niveau sets $\left\{x:F(x)\le\alpha\right\}$ are compact
Apr
13
reviewed Leave Open Find the distance travelled by $P$ before it changes direction. (Mechanics)
Apr
13
reviewed Leave Open How many natural numbers less than $10^{2015}$ have their digits in non-decreasing order?
Apr
13
reviewed Leave Open Quadratic Integers in $\mathbb Q[\sqrt{-5}]$
Apr
13
reviewed Close I am going to learn these Mathematics Topics. I need advice and suggestions please .
Apr
13
reviewed Close Error in using Matlab detectSurffeatures
Apr
13
reviewed Leave Closed How do mathematicians find formulas?
Apr
13
reviewed Leave Open Variant on Law of Iterated Conditioning
Apr
13
reviewed Looks OK Representative Pedagogical Examples of Groups, Real Functions, Modules, etc.
Apr
13
reviewed Edit Transformation of graphs
Apr
13
revised Transformation of graphs
added 84 characters in body
Apr
13
reviewed Close An easy question with integer numbers
Apr
13
reviewed Leave Open Determine the Taylor expansion for the solution of the differential equation