\(
\newcommand{\P}[]{\unicode{xB6}}
\newcommand{\AA}[]{\unicode{x212B}}
\newcommand{\empty}[]{\emptyset}
\newcommand{\O}[]{\emptyset}
\newcommand{\Alpha}[]{Α}
\newcommand{\Beta}[]{Β}
\newcommand{\Epsilon}[]{Ε}
\newcommand{\Iota}[]{Ι}
\newcommand{\Kappa}[]{Κ}
\newcommand{\Rho}[]{Ρ}
\newcommand{\Tau}[]{Τ}
\newcommand{\Zeta}[]{Ζ}
\newcommand{\Mu}[]{\unicode{x039C}}
\newcommand{\Chi}[]{Χ}
\newcommand{\Eta}[]{\unicode{x0397}}
\newcommand{\Nu}[]{\unicode{x039D}}
\newcommand{\Omicron}[]{\unicode{x039F}}
\DeclareMathOperator{\sgn}{sgn}
\def\oiint{\mathop{\vcenter{\mathchoice{\huge\unicode{x222F}\,}{\unicode{x222F}}{\unicode{x222F}}{\unicode{x222F}}}\,}\nolimits}
\def\oiiint{\mathop{\vcenter{\mathchoice{\huge\unicode{x2230}\,}{\unicode{x2230}}{\unicode{x2230}}{\unicode{x2230}}}\,}\nolimits}
\)
Related to counting, countabiliy
Diagonal
The goal is to get formulas for the following:
\(\displaystyle
\begin{bmatrix}
0 & 2& 5& 9&\\
1 & 4& 8& &\\
3 & 7& & &\\
6 & & & &\\
\end{bmatrix}
\)
This can be visualized as:
\(\displaystyle
\begin{bmatrix}
& & & &\\
& & 5& &\\
& 2& 4& &\\
0 & 1 & 3& ... &\\
\end{bmatrix}
\)