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Oct
10
comment Show that if a positive integer $ n $ is composite then $ R(n) = \frac{10^{n}-1}{9}= 111…11 (n times) $ is composite
This is fine for $n\geq 2$
Oct
10
revised Show that if a positive integer $ n $ is composite then $ R(n) = \frac{10^{n}-1}{9}= 111…11 (n times) $ is composite
added 3 characters in body
Oct
10
revised Show that if a positive integer $ n $ is composite then $ R(n) = \frac{10^{n}-1}{9}= 111…11 (n times) $ is composite
added 2 characters in body
Oct
9
revised $AB$ is not invertible
n was used elsewhere as something else
Oct
7
comment Show that $f$ is a polynomial if it's the uniform limit of polynomais
You are right. ${}$
Oct
7
revised Show that $f$ is a polynomial if it's the uniform limit of polynomais
Formatting
Oct
7
comment What is the meaning of this notation in algebraic geometry (from /): $k\left[x_{1},\ldots,x_{r}\right]\mathbf{/\left(f_{1},\ldots,f_{r}\right)}$?
@azarel add it as an asnwer, I'll upvote it.
Oct
7
comment Inverse of matrix sum of identity and outer product
If $u,v\in\Bbb R^n$ then $uv^T$ is a number, or do you mean $u,v\in\Bbb R^{n\times 1}$.
Oct
7
comment Is the space $B([a,b])$ separable?
$B([a,b])$, surely it's a typo.
Oct
7
comment Proving linear independence of infinite set (monomials)
@Magdiragdag That's the case if the coefficients of the polynomials come from a finite field. OP is considering polynomial functions over $\Bbb R$ or $\Bbb C$ (question is not very clear).
Oct
7
revised Proving linear independence of infinite set (monomials)
Formatting
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.