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Jul
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comment $\limsup$ and cluster points
In fact, you can show that 1) $\lim \sup x_n$ is a cluster point of $(x_n)$, and that 2) it's greater than any other cluster point of $(x_n)$. That is, $\sup C$ is actually $\max C$. You could try to construct a sequence that converges to $\lim \sup x_n$ (then it's easy to see that $\lim \sup x_n$ is a cluster point of $(x_n)$).
Jun
24
comment Modular arithmetic for negative numbers
@anon I agree, but I understood that the OP was uncomfortable with having a negative right-hand side, and this is a way to avoid that.
Jun
24
comment Counting number of ways of splitting a card deck
Note that sometimes it is acceptable to give an answer in terms of factorials and combinatorial numbers, so you might not actually have to perform the multiplication.
Jun
24
revised Counting number of ways of splitting a card deck
fixed typos, reworded a bit
Jun
24
suggested approved edit on Counting number of ways of splitting a card deck
Jun
24
suggested rejected edit on What is a formal definition of series?
Jun
24
comment Modular arithmetic for negative numbers
... in the equation). Now, to find the values of $m$ that satisfy the congruence, if $k$ is small you could just try some values.
Jun
24
comment Modular arithmetic for negative numbers
With congruences you can always add any multiple of the modulus, since they're all equivalent to $0$. In this case, since $m^2 \equiv -1 \pmod{2k+1}$, and $2k+1 \equiv 0 \pmod{2k+1}$, we have $$m^2 \equiv -1 = -1 + 0 \equiv -1 + 2k+1 = 2k \pmod{2k+1}$$ It's a string of equalities and equivalences, consider each $\equiv$ or $=$, and try to understand what happens in the passage from the left side to the right side of each $\equiv$ or $=$. In any case, this is only one thing you could do (to avoid the negative number; although you should be comfortable with having a negative right-hand side ...
Jun
24
revised Modular arithmetic for negative numbers
latex, capital letter
Jun
24
comment Modular arithmetic for negative numbers
You can note that $m^2 = -1 \equiv (2k+1)-1 = 2k \pmod{2k+1}$.
Jun
24
suggested approved edit on Modular arithmetic for negative numbers
Jun
24
revised Eigenvectors of a matrix and its diagonalization
fixed typos
Jun
24
suggested approved edit on Eigenvectors of a matrix and its diagonalization
Jun
24
revised A proof in number theory dealing with modular congruences.
added 122 characters in body
Jun
24
comment A proof in number theory dealing with modular congruences.
@Iyengar Never mind :-)
Jun
24
comment A proof in number theory dealing with modular congruences.
@Iyengar I thought about that, but I'm answering the question that the OP is asking, and since answering a question in the comments is in fact disencouraged, I believe I'm following the guidelines of the site (regardless of the length of the answer and the effort that I put into it). If I'm wrong about this point, I welcome any corrections.
Jun
24
revised Generating the Sorgenfrey topology by mappings into $\{0,1\}$, and on continuous images of the Sorgenfrey line
added latex, fixed formatting