T. Eskin
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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