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Sep
4
comment Prove that the binary relation “is a subset of” is a…
The relation $\subseteq$ is a partial order on the class of all sets, you can immediately verify the defining conditions. As the class of all sets fails to be a set, we do not get a poset this way. However, if we work only with subsets of a "unversal" set, then the universal set together with $\subseteq$ is a poset.
Sep
4
answered How to interpret fractional number of bits of precision
Sep
4
answered Can you help me complete the proof?
Sep
4
comment How do you solve $f'(x) = f(f(x))$?
@davincisghost Yes, after your original comment I was of course looking for nontrivial holomorphic solutions. In a way $\infty$ is a solution of $2k=k-1$ :)
Sep
3
comment Compressing an image by merging pixels
Any vertex of the shape must be a vertex of a rectangle, hence with a shape with so many vertices ("round" boundaries), it is fat and easy and almost optimal to make scanlines row by row and see if sometimes consecutive lines match.
Sep
3
comment Can ∅, as being an element of a set, be handled as any other element?
@HenningMakholm There was, back then, in the title "[t]he union of ∅ with any other element or Set"
Sep
3
comment Can ∅, as being an element of a set, be handled as any other element?
$A\cup \emptyset = A$ for all $A$
Sep
3
comment Predictiction / extrapolation of values
With the box doing more or less the same all the time, predicting the current average looks like a good idea ...
Sep
2
revised What is the sprague-grundy value of these games?
added 1827 characters in body
Sep
2
comment What is the sprague-grundy value of these games?
Oh, now I see your point - wait.
Sep
2
comment What is the sprague-grundy value of these games?
@WardBeullens I'm not sure. The way I see it, "$+$" is the case $N=1$ and "$\vee$" is the case $N=2$, isn't it? The first part of my answer rephrases the WP article, and I don't see what you are asking beyond that. The second part discusses why this is not directly applicable to A Game of Knights (even if you never mentioned that), where the sub-games are equivalent but not equal to nimbers.
Sep
2
answered What is the sprague-grundy value of these games?
Sep
2
comment Optimal strategy for this Nim generalisation?
@MJD Then the real question is: Given heap sizes $n_1, \ldots, n_m$ and $N$, determine $n$ that is equivalent to this game.
Sep
2
comment Optimal strategy for this Nim generalisation?
@calculus The well-known strategy is to XOR all pile sizes and make a move that makes the XOR zero (if it is already zero, you lose).
Sep
2
comment Optimal strategy for this Nim generalisation?
That's a good question - I wish I had known the answer last week :). Wait, are you the Ward Beullens who also took part in hackerrank's weekly?
Sep
2
comment How do you solve $f'(x) = f(f(x))$?
Assume $f$ holomorphic and $f(0)=0$, say $0$ is a root of order $k$. Then $f(f(x))$ has a root of order $2k$ and $f'$ has a root of order $k-1$. Oops.
Sep
2
comment A question about $f(f(x))=x^2+x$
If you want $f$ to be smooth and $f(0)=0$ and $f'(0)>0$, then the power series should be just what you want ...
Sep
2
answered Conclude behaviour of holomorphic function on interior from behaviour on boundary - by the example of Theta function
Sep
2
comment Let $\displaystyle D= \{z: |x|<1\}$ which of the following is correct
Do you mean $\{\,z=x+iy:|x|<1\,\}$ or $\{\,z=x+iy:|z|=\sqrt{x^2+y^2}<1\,\}$?
Sep
1
answered Prove by induction that $n!+n \geq 2^n$