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Nov
27
awarded  Popular Question
Nov
6
accepted Prove that the number of pairs of edges that cross in a drawing of $K_n$ is at least $\frac{1}{5}\binom{n}{4}$ (for $n\geq 5$)
Nov
6
comment Prove that the number of pairs of edges that cross in a drawing of $K_n$ is at least $\frac{1}{5}\binom{n}{4}$ (for $n\geq 5$)
@JaycobColeman good point, done.
Nov
6
revised Prove that the number of pairs of edges that cross in a drawing of $K_n$ is at least $\frac{1}{5}\binom{n}{4}$ (for $n\geq 5$)
added 54 characters in body
Nov
6
asked Prove that the number of pairs of edges that cross in a drawing of $K_n$ is at least $\frac{1}{5}\binom{n}{4}$ (for $n\geq 5$)
Oct
23
answered Proof by Induction for a recursive sequence and a formula
Oct
20
answered What is that sign in the context of vectors?
Oct
18
accepted Prove that flow is a linear combination of flow cycles and flow paths
Oct
18
asked Prove for a connected graph $G=(V,E)$, $\kappa(G)=1+\min_{v\in V}\kappa(G-v)$
Oct
17
answered Covering a chess board with $2$ missing places with $31$ dominoes
Oct
17
comment Covering a chess board with $2$ missing places with $31$ dominoes
[you may find this article useful](en.wikipedia.org/wiki/Matching_(graph_theory)) although it may be a little technical.
Oct
17
answered Is 9/1 an improper fraction?
Oct
17
comment Is 9/1 an improper fraction?
@BrianM.Scott fair, but in my experience working with students at the high school level, they don't necessarily see that $2\frac{1}{3}$ is the same as $2+\frac{1}{3}$. Then you end up with kids mechanically, mindlessly "converting" improper fractions to proper fractions, adding, and then reconverting back into proper fractions in order to evaluate, say, $2\frac{1}{3}+3\frac{2}{3}$, instead of recognizing that they may as well just go $2+3+\frac{1}{3}+\frac{2}{3}$. This is all very much beside the main point though I guess.
Oct
17
comment Is 9/1 an improper fraction?
@Mike almost—students are actually taught to write $8/3$ as $2\frac{1}{3}$, i.e. to omit the plus sign. This is IMO disastrously bad notation and the "proper" v. "improper" nomenclature is inappropriate and it's just a bad practice all around.
Oct
17
comment geometric description of subsets that form bases in $\mathbb R^2$ and $\mathbb R^3$
@CassandraFairWilliams Ah okay, it means the same number of elements. So the question is: if $B_1=\{\mathbf{u}_1,\dots\mathbf{u}_j\}$ and $B_2=\{\mathbf{v}_1,\dots\mathbf{v}_k\}$ are both bases for the same space, then is it necessarily true $j=k$? Do you have any intuition about what the answer might be?
Oct
17
comment I have a recursively defined function, and another function involving powers of a matrix. How can I show that they are equal?
Awesome. I was thinking that maybe there was some argument that could me made that matrix multiplication is like applying the same function over and over again and so those are actually the same thing, but I don't know if that works. This works perfectly though.
Oct
17
accepted I have a recursively defined function, and another function involving powers of a matrix. How can I show that they are equal?
Oct
17
comment I have a recursively defined function, and another function involving powers of a matrix. How can I show that they are equal?
right, I did write that part. My question is more about the implicit assertion that $A^l=w_l$, i.e. raising $A$ to a power is the same as applying $w$ $l$ times.
Oct
17
answered geometric description of subsets that form bases in $\mathbb R^2$ and $\mathbb R^3$
Oct
17
comment geometric description of subsets that form bases in $\mathbb R^2$ and $\mathbb R^3$
Do you know what a basis is?