Binomial Coefficient with Zero/Integer Coefficients

Theorem

$\forall n \in \N: \dbinom n 0 = 1$

where $\dbinom n 0$ denotes a binomial coefficient.

From the definition:

$\ds \binom n 0$

$=$

$\ds \frac {n!} {0! \ n!}$

Definition of Binomial Coefficient

$\ds $

$=$

$\ds \frac {n!} {1 \cdot n!}$

Definition of Factorial of $0$

$\ds $

$=$

$\ds 1$

$\blacksquare$

1964: Milton Abramowitz and Irene A. Stegun: Handbook of Mathematical Functions ... (previous) ... (next): $3$: Elementary Analytic Methods: $3.1$ Binomial Theorem etc.: Binomial Coefficients: $3.1.5$
1964: A.M. Yaglom and I.M. Yaglom: Challenging Mathematical Problems With Elementary Solutions: Volume $\text { I }$ ... (previous) ... (next): Problems
1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 19$: Combinatorial Analysis: Theorem $19.10$
1971: Robert H. Kasriel: Undergraduate Topology ... (previous) ... (next): $\S 1.18$: Sequences Defined Inductively: Exercise $3 \ \text{(a)}$
1992: Larry C. Andrews: Special Functions of Mathematics for Engineers (2nd ed.) ... (previous) ... (next): $\S 1.2.4$: Factorials and binomial coefficients: $1.27$