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 Oct7 revised Proving linear independence of infinite set (monomials) Formatting Oct7 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 $F[x]$. Oct5 comment Is the space $B([a,b])$ separable? Fine. Still my notes ask to prove that space it's separable. Oct2 revised Is the space $B([a,b])$ separable? added 39 characters in body Oct2 revised Decomposing Countable Union of Measurable Sets added 200 characters in body Oct2 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. Oct2 answered Decomposing Countable Union of Measurable Sets Oct2 revised How to plot $r^2 = 36\cos(2\phi)$ in Cartesian coordinates? added 4 characters in body; edited title Oct1 revised Why are real numbers useful? added 1 character in body Oct1 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. Oct1 answered $AB$ is not invertible Oct1 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 Oct1 revised $AB$ is not invertible Improving title Oct1 comment Couple basic linear algebra questions (please help) See here Sep30 awarded Explainer Sep30 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? Sep30 revised Proof that $-v = (-1)*v$ edited title Sep29 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. Sep29 comment Inverse of matrix sum of identity and outer product Matrix $B$ is the inverse of matrix $A$ if and only if... Sep29 awarded Revival