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3h
reviewed Approve Induced topologies by Metric Spaces continuous
Apr
26
answered Monotone Convergence Theorem for nonnegative functions (not quite a decreasing sequence)
Apr
26
comment Is $(0, \infty)$ closed in $\mathbb{R}-0$?
Not all closed sets are compact. And not all non-closed sets are open.
Apr
25
comment Continuous function differentiable almost everywhere, show f' is measurable
@corkol. composition of continuous functions
Apr
25
comment for $x∈[1,3]$ , let $h(x)$ be value of shadow shown below, find $h'(x)$
@suri. What you wrote there in the comment is just the definition of $f'(a)$. Search for fundamental theorem of calculus.
Apr
22
comment open\closed and disjoint sets under R2
@havakok. The continuous functions are $(x,y)\mapsto y-\frac{1}{x}$ and $(x,y)\mapsto x$.
Apr
22
comment open\closed and disjoint sets under R2
@havakok. If $X$ and $Y$ are two sets, $X\setminus Y$ is the set of elements that are in $X$ but not in $Y$.
Apr
22
revised open\closed and disjoint sets under R2
edited tags
Apr
22
answered open\closed and disjoint sets under R2
Apr
22
comment Find a solution to $z+e^{-z}=a$ where $a>1$.
Numerical approximations allowed or only closed form solutions?
Apr
21
comment Prove that dim(U + V ) ≤ dim U + dim V .
@user6156388. Take $U=V$ for example. Then $U+V=U$ so $dim(U+V)=dim(U)<2dim(U)=dim(U)+dim(V)$. And $U$ can be any non-empty subspace of any non-empty vector space. As another non-trivial example, take $W=\Bbb{R}^{3}$ and $U$ a line that is inside a plane $V$. E.g. $V=\{(x,z,y):z=0\}$ and $U=\{(x,y,z):y=0,\;z=0\}$. Then $U+V=V$, so $dim(U+V)=dim(V)=2<3=dim(U)+dim(V)$.
Apr
19
comment Prove that dim(U + V ) ≤ dim U + dim V .
@user6156388. Correct. And there is no other case when it would occur. In that instance, obviously U and V don't have to share a basis vector given an arbitrary basis for both, but it must be the case that you can find a vector that is a basis vector for both U and V.
Apr
19
answered Prove that dim(U + V ) ≤ dim U + dim V .
Apr
18
comment Is a space metric on the positive real numbers not complete?
Note that $\lim_{x\to\infty}\frac{1}{x}$ has to be interpreted in terms of the metric $d$ and not in terms of the usual metric on $\Bbb{R}$.
Apr
14
reviewed Reject Dual curve of an algebraic curve in affine coordinates
Apr
14
reviewed Reject Convergence or divergence of $\sum \frac{3^n + n^2}{2^n + n^3}$
Apr
14
reviewed Approve System of nonhomogenous differential equations - Undetermined coefficients
Apr
14
reviewed Reject Is there a symbol for always less than (or just always?)
Apr
14
reviewed Edit Convergence of a complex series for some values of z
Apr
14
revised Convergence of a complex series for some values of z
notation issues