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Oct
7
comment Proving linear independence of infinite set (monomials)
A set is linearly independent if and only if all it's finite subsets are linearly independent. If by the set of monomials you mean $\{1,x,x^2,\ldots,\}$ then yes, they are linearly independent. To prove it you can proof this more general statement: Let $S$ be a set of non zero polynomials over a field $F$. If there are no two polynomials with the same degree, then $S$ is a linearly independent subset of $F[x]$.
Oct
5
comment Is the space $B([a,b])$ separable?
Fine. Still my notes ask to prove that space it's separable.
Oct
2
revised Is the space $B([a,b])$ separable?
added 39 characters in body
Oct
2
revised Decomposing Countable Union of Measurable Sets
added 200 characters in body
Oct
2
comment Decomposing Countable Union of Measurable Sets
You're right. I didn't see the "countably many measurable sets" and focused in the "finite outer measure" part.
Oct
2
answered Decomposing Countable Union of Measurable Sets
Oct
2
revised How to plot $r^2 = 36\cos(2\phi)$ in Cartesian coordinates?
added 4 characters in body; edited title
Oct
1
revised Why are real numbers useful?
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Oct
1
comment How to proof the following function is always constant which satisfies $f\left( x \right) + a\int_{x - 1}^x {f\left( t \right)\,dt} $?
I didn't read the question correctly. Now I understand.
Oct
1
answered $AB$ is not invertible
Oct
1
comment How to prove that $\det\left[\pmatrix{u_1 & v_1\\ u_2 & v_2\\ u_3 & v_3}\pmatrix{s_1 & s_2 & s_3\\ t_1 & t_2 & t_3}\right]=0$?
In general, we have this
Oct
1
revised $AB$ is not invertible
Improving title
Oct
1
comment Couple basic linear algebra questions (please help)
See here
Sep
30
awarded  Explainer
Sep
30
comment How to proof the following function is always constant which satisfies $f\left( x \right) + a\int_{x - 1}^x {f\left( t \right)\,dt} $?
Can you expand on the second line of your answer?. If one already knows that the posed function is a constant one, then of course your argument it's true, but without that knowledge, how?
Sep
30
revised Proof that $-v = (-1)*v$
edited title
Sep
29
comment Problem on matrices : $\dim E\leq n^2-(n-r)^2-1$
$M_n(\Bbb R)$ is a subspace which contains non invertible matrices and such that the bound does not hold.
Sep
29
revised Question on topology and Zorn's lemma
added 2 characters in body
Sep
29
comment Inverse of matrix sum of identity and outer product
Matrix $B$ is the inverse of matrix $A$ if and only if...
Sep
29
awarded  Revival