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 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? Oct 17 asked I have a recursively defined function, and another function involving powers of a matrix. How can I show that they are equal? Oct 8 comment Given $f(x)$ its inverse function, domain and range @Assad well, an inverse function does not always exist. But where one does, yes it holds true. Oct 8 answered If a linear system has no free variables, then it is consistent: Why is the statement false? Oct 8 answered Given $f(x)$ its inverse function, domain and range Oct 8 answered How do I proove the symmetry of Metric space? Oct 8 asked Prove that flow is a linear combination of flow cycles and flow paths Oct 7 comment Calculus remark I forgot. You're going to need to put some more restrictions on $X$. For instance, this clearly doesn't hold for the empty set. Or the set of all integers. Or the set of negative real numbers. Or $[0,1] \backslash \{x:x=1/n,n\in\mathbb{N}\}$. Etc. But there's something there if you refine it a little bit. Oct 5 awarded Yearling Oct 5 accepted Help with a step in Diestel's proof of Tutte's theorem in Graph Theory Oct 5 asked Help with a step in Diestel's proof of Tutte's theorem in Graph Theory