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Mar
25
answered Slice, projection, contour: A terminology question.
Mar
25
comment Why hyperreal numbers are built so complicatedly?
@RossMillikan, that field is the field of Formal Laurent series. It doesn't have the "elementary extension" property that we would like.
Mar
24
answered Extending the Ordinals analogously to the Integers
Mar
24
answered Why hyperreal numbers are built so complicatedly?
Mar
24
comment Why hyperreal numbers are built so complicatedly?
I think what you intended is a true statement about the hyperreals, so that's not really an avoided problem.
Mar
22
comment What function would do this
Every function on the integers of period 2 is a linear combination of the powers of the two second roots of unity. i.e. It's $a(-1)^n+b(1)^n$ for some $a$ and $b$. Matt Samuel's answer exhibits $a$ and $b$. Crash's answer elaborates on Henning Makholm's comment: saying what a function does on every input is defining that function. We consider $\cos(n\pi)$, $(-1)^n$, and "the function on the integers that outputs $-1$ when the input is odd and $1$ otherwise" to all refer to the same function.
Mar
22
comment Do any of these sequences have infinitely-many distinct iterates under run-length substitution?
@user48481 A run is a sequence of adjacent repeated values. I wouldn't have thought of this as a technical term until now, when I couldn't find this definition in a dictionary.
Mar
21
answered Dimension Theorem Corollary
Mar
19
answered Cross products and determinants in $\mathbb{R}^3$
Mar
15
answered countable subset of surreal games
Mar
15
comment Why can a Nim sum be written as powers of 2?
@BrianM.Scott Your first and third links are identical. www1.icsi.berkeley.edu/~ejf/pfiles/nimgroups.pdf is another PDF about this question (or at least a very related one).
Mar
15
answered Optimal strategy in a match picking game
Mar
15
comment Sorting circles sizes with points in integers lattice
Also, it's not quite the same thing, but you may be interested in the rational parametrization of the unit circle and the consideration of those points as a group‌​.
Mar
15
comment Sorting circles sizes with points in integers lattice
"Then I find the smallest radius for boxes of width W+1 and reject from the sorted list all the findings greater than W+1 smallest." I'm not sure I understand what this part is saying.
Mar
15
comment Settlers of Catan Boards possibilities
There are only 6 ways to rotate the board that put corners on corners. And I don't think it's obvious that you can just divide by the number or rotations to get the answer.
Mar
15
answered Settlers of Catan Boards possibilities
Mar
10
answered Why can a Nim sum be written as powers of 2?
Mar
8
revised What is the condition for the first root of a cubic function to be positive?
added important "real coefficients" assumption
Mar
8
comment What is the condition for the first root of a cubic function to be positive?
@Taladris In the cubic case, when you combine it with the discriminant, Descartes' Rule of Signs can be used to find the exact the number of positive roots. When the discriminant is positive so that there's only one real root, the real root is given by $x_1$, so the Rule of Signs can tell you if $x_1$ is positive in that case, but of course not in the three-real-root case.
Mar
8
answered What is the condition for the first root of a cubic function to be positive?