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1d
comment Deduce the Bolzano-Weierstrass Theorem from the Heine-Borel Theorem
@flapjackery Not necessarily. For example if the open cover is such that each interval contains one $x_n$ then it will contain an infinite number of the $x_n$, as long as there are infinite intervals in the cover.
1d
answered Deduce the Bolzano-Weierstrass Theorem from the Heine-Borel Theorem
Oct
17
awarded  Nice Answer
Oct
14
comment Finitely additive function on an infinite set, s.t., $m(A)=0$ for any finite set and $m(X)=1$ (constructive approach)
Different exercises, different questions. Would be better.
Oct
14
answered Graph of measurable function has measure 0 in the product measure space
Oct
10
revised Does there exist such sequence?
added 23 characters in body
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 Let {b_n} be a bounded sequence of nonnegative numbers and 0 <= r < 1. Let {s_n} = b1r + … + bnr^n. Prove {s_n} is monotonically decreasing.
It's not monotonically decreasing. You obtain $s_{n+1}$ by adding a non negative quantity, namely $b_{n+1}r^{n+1}$ so you have $s_n\leq s_{n+1}$
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.