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 Dec 31 reviewed Approve To determine Nullity of $T$ Dec 31 comment A generalized derivative @user62029 I have a copy of this one. Take a look at it. Dec 31 accepted Does the maximum cut implies the minimum flow? Dec 31 accepted How do we define interior and exterior of a geometric figure? Dec 31 accepted How to solve this kind of problem? Dec 31 accepted How to use $\binom a k = \frac{\alpha(a-1)(a-2)\cdots(a-k+1)}{k(k-1)(k-2)\cdots 1}$ to check that ${-1\choose 0}=1$? Dec 31 comment How $(r-k){r \choose r-k}$ becomes $r{r-1 \choose r-k-1}$? Hey, I've finally been able to understand it. I've posted it as an answer below. Dec 31 answered How $(r-k){r \choose r-k}$ becomes $r{r-1 \choose r-k-1}$? Dec 28 asked How $(r-k){r \choose r-k}$ becomes $r{r-1 \choose r-k-1}$? Dec 27 accepted What is the generating function to calculate the number of functions $f:\{1,2,3,4,5,6,7,8,9,10\}\to\{1,2,3,4,5,6,7\}$ with $|Im(f)|=4$? Dec 27 comment What is the generating function to calculate the number of functions $f:\{1,2,3,4,5,6,7,8,9,10\}\to\{1,2,3,4,5,6,7\}$ with $|Im(f)|=4$? But anything that is expressed with one could also be expressed with the other, right? Disregarding if they have good closed expressions. Dec 27 comment How to use $\binom a k = \frac{\alpha(a-1)(a-2)\cdots(a-k+1)}{k(k-1)(k-2)\cdots 1}$ to check that ${-1\choose 0}=1$? I just need to do that? There's nothing that could be made with that definition so that it would result in ${-1 \choose 0}=1$? Dec 27 asked How to use $\binom a k = \frac{\alpha(a-1)(a-2)\cdots(a-k+1)}{k(k-1)(k-2)\cdots 1}$ to check that ${-1\choose 0}=1$? Dec 27 accepted How to use $\binom a k = \frac{\alpha(a-1)(a-2)\cdots(a-k+1)}{k(k-1)(k-2)\cdots 1}$ to check that ${-n \choose -n}=0$? Dec 27 comment How to use $\binom a k = \frac{\alpha(a-1)(a-2)\cdots(a-k+1)}{k(k-1)(k-2)\cdots 1}$ to check that ${-n \choose -n}=0$? Yes. Thanks. I thought it would make some kind of sense to use $\binom a k = \frac{\alpha(a-1)(a-2)\cdots(a-k+1)}{k(k-1)(k-2)\cdots 1}$ alone. I am having lectures on introductory combinatorics and my professor told us that $k,x$ only make sense when non-negative integers with $k\geq x$, then I started reading Knuth/Patashnik/Graham's Concrete Mathematics and there he uses almost arbitrary $k,x$'s. I'm on an exploratory work on this new concepts. Dec 27 asked How to use $\binom a k = \frac{\alpha(a-1)(a-2)\cdots(a-k+1)}{k(k-1)(k-2)\cdots 1}$ to check that ${-n \choose -n}=0$? Dec 27 accepted Why ${-1\choose 3}=-1$? Dec 27 accepted What is the convolution here? Dec 27 comment Why ${-1\choose 3}=-1$? That's it. It makes more sense to see $\alpha - (k-1)$. This way, it seems that $(k-1)$ is entirely on the plot. Seeing $a-k+1$ is like $k$ was the protagonist and $1$ have nothing to do with it. Dec 27 comment Why ${-1\choose 3}=-1$? I don't get it. So instead of reaching $k$, I should reach $k-1$?