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Jul
23
comment Why does this graph only the positive side
Hint: Do you think that $\sqrt[4]{x^2}=x^{2/4}=x^{1/2}=\sqrt x$ for all real numbers $x$?
Jul
23
answered Question concerning how a map extends to a homomorphism.
Jul
22
comment Where's the problem with a false “proof”: $\;1^0 = 1^2 \overset{?}\implies 0 = 2$
Apparently it is. Otherwise, we'd have $0=2$.
Jul
22
comment Does the boundaries of non-disjoint sets in Euclidean space have common element?
Well, you need to add a few conditions. For example if the sets are open, not disjoint, not contained in one another, and connected ...
Jul
22
comment Primitive-recursive functions and polynomial equations
Unless $K(m,n)$ is constant, $\prod_{i=0}^{K(n,m)}(P(n,m,i)-Q(n,m,i))$ is not of the form $P(n,m)-Q(n,m)=0$.
Jul
22
answered Primitive-recursive functions and polynomial equations
Jul
22
comment Proving some properties of $\Bbb N$ without using recursion
@Graduate I don't think that William wanted to object against referencing the axioms, but against referencing them by a local obscure notation. Saying Axiom of Infinity or simply INF instead of ZF7, Axiom of Power Set or simply POW instead of ZF4, Axiom Schema of Separation or simply SEP instead of ZF5 would have made a reference to the axioms as intended - and the reader would know which are meant.
Jul
22
answered Proving some properties of $\Bbb N$ without using recursion
Jul
22
answered Let $V$ be a vector space, $W$ a supspace. Can we conclude that $W\oplus (V/W)$ and $V$ are isomorphic?
Jul
22
answered About the subspace of polynomial vector space
Jul
22
answered May a monoid have two disjoint submonoids?
Jul
22
awarded  recreational-mathematics
Jul
22
awarded  Good Answer
Jul
21
awarded  Nice Answer
Jul
21
revised Pick a smart function
added 685 characters in body
Jul
21
answered Pick a smart function
Jul
21
comment Pick a smart function
Is there a reason for the parentheses on the right hand side? Should there possibly be a $-\cos x$ in one of the two equations?
Jul
21
comment Seminorm proof of a function
Just verify the defining conditions (which is straightforward)
Jul
21
answered Integral expression $P=x^3+x^2+ax+1$, …
Jul
21
comment proving closure of a subset
And as seen there, simply writing down what one has to show almost completes the proof.