ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Subset
N-subset
Set of N-subsets
Definition D2167
Binomial coefficient
Formulation 2
Let $n, m \in \mathbb{N}$ each be a D996: Natural number.
The binomial coefficient with respect to $(n, m)$ is the D996: Natural number \begin{equation} \binom{n}{m} : = |\mathcal{P}_m \{ 1, \ldots, n \}| \end{equation}
Formulation 3
Let $n, m \in \mathbb{N}$ each be a D996: Natural number.
The binomial coefficient with respect to $(n, m)$ is the D996: Natural number \begin{equation} \binom{n}{m} : = \# \left\{ E \subseteq \{ 1, \ldots, n \} : |E| = m \right\} \end{equation}
Children
Central binomial coefficient
Results
R3611
Complement property of binomial coefficient
Pascal's rule
Real arithmetic expression for binomial coefficient
Real binomial theorem for exponent five
Real binomial theorem for exponent four
Real binomial theorem for exponent seven
Real binomial theorem for exponent six
Real binomial theorem for exponent three
Conjectures
Singmaster's conjecture