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Mar
11
answered How do I find the set $\bigcup_{k = 2}^{10}A_k$ if $A_k = [k, 2k-1]$
Mar
11
comment Limit of a sequence: $a_n \le b_n \le c_n$
@user1799252. We only choose max here because we know that certain conditions of our interest are true for each of the cases $n\geq N_0$, $k\geq N_1$, and for $j\geq N_2$. Now we want all these conditions to hold simultaneously, so if $n\geq \max\{N_0, N_1, N_2\}$ then certainly $n\geq N_0$ and $n\geq N_1$ and $n\geq N_2$.
Mar
11
answered Show that a series is not uniformly convergent
Mar
11
answered Limit of a sequence: $a_n \le b_n \le c_n$
Mar
11
comment What does it mean for f([x])=[2x] for a function mapping R/Z to R/Z?
@nene. Basically by looking at the equation $f([x])=f([y])$ you are looking at all the different equivalence classes $[x]$ and $[y]$ that get mapped to the same same equivalence class. I.e. at the preimage of that particular equivalence class. Solving the relationship between $x$ and $y$ gives you the selection of all such classes. Both ways, this and Tim's, gives you a way to conclude the answer. It's just a matter of preference I would say.
Mar
11
reviewed Approve equicontinuity tag wiki excerpt
Mar
11
reviewed Approve triangulation tag wiki
Mar
11
reviewed Reject triangulation tag wiki excerpt
Mar
11
reviewed Reject simplicial-complex tag wiki excerpt
Mar
11
reviewed Reject Probability: Store opening time
Mar
11
revised What does it mean for f([x])=[2x] for a function mapping R/Z to R/Z?
added 91 characters in body
Mar
11
answered What does it mean for f([x])=[2x] for a function mapping R/Z to R/Z?
Mar
10
comment Show that $(\mathbb{R}^\infty,\lVert\rVert)$ is not complete space.
@captain lama. $\mathbb{R}^{n}$ is countable dimensional normed space and it's complete.
Mar
10
awarded  real-analysis
Mar
10
comment Classify each of the following sets as open, closed, or neither
@mathhelpplease. Right, but including the point $3$ also. So $(2,3]\cup [5,6)$. Now, do you think this set would be open or closed? Depending on your definition of these two concepts, could you work out an argument that prove your statement? Think first whether either $(2,3]$ or $[5,6)$ are closed or open themselves.
Mar
10
comment Classify each of the following sets as open, closed, or neither
@mathhelpplease. So the set of $(3)$ is the intersection of those two sets. Is that open or closed?
Mar
9
revised Classify each of the following sets as open, closed, or neither
added 6 characters in body; edited tags
Mar
9
answered Classify each of the following sets as open, closed, or neither
Mar
9
comment If, $\forall n\in\mathbb{N}$, $\lvert x_{n+1} - x_n \lvert\le a^n$ (for $a\in (0,1)$), then $x_n\to x$
@sequence. The first inequality is triangle inequality applied $m-n$ times and the equality after that is just expressing the partial sum from $n$ to $m-1$ as the difference of the same sum by noticing that it is the same as from $0$ to $m-1$ minus from $0$ to $n-1$. Then just use the geometric series formula.
Mar
9
revised If, $\forall n\in\mathbb{N}$, $\lvert x_{n+1} - x_n \lvert\le a^n$ (for $a\in (0,1)$), then $x_n\to x$
added 316 characters in body