# 1

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## Number

$1$ (one) is:

The immediate successor element of zero in the set of natural numbers $\N$

The only (strictly) positive integer which is neither prime nor composite

The only (strictly) positive integer which is a divisor of every integer

### $0$th Term

The $0$th (zeroth) power of every non-non-zero number:
$\forall n: n \ne 0 \implies n^1 = 1$

The $0$th term of Göbel's sequence, by definition

The $0$th term of the $3$-Göbel sequence, by definition

The $0$th and $1$st Catalan numbers:
$\dfrac 1 {0 + 1} \dbinom {2 \times 0} 1 = \dfrac 1 1 \times 1 = 1$
$\dfrac 1 {1 + 1} \dbinom {2 \times 1} 1 = \dfrac 1 2 \times 2 = 1$

The $0$th and $1$st Bell numbers

### $1$st Term

The $1$st (strictly) positive integer

The $1$st (strictly) positive integer

The $1$st (positive) odd number
$1 = 0 \times 2 + 1$

The $1$st number to be both square and triangular:
$1 = 1^2 = \dfrac {1 \times \paren {1 + 1}} 2$

The $1$st generalized pentagonal number:
$1 = \dfrac {1 \paren {3 \times 1 - 1} } 2$

The $1$st highly composite number:
$\tau \paren 1 = 1$

The $1$st special highly composite number

The $1$st highly abundant number:
$\sigma \paren 1 = 1$

The $1$st superabundant number:
$\dfrac {\sigma \paren 1} 1 = \dfrac 1 1 = 1$

The $1$st almost perfect number:
$\sigma \paren 1 = 1 = 2 - 1$

The $1$st factorial:
$1 = 1!$

The $1$st superfactorial: