sequence

A sequence is a function is any function \( f \) such that \( \text{dom} \left ( f \right ) = \mathbb{N}_{1} \). With this in place, we can consider the \( n \)-th element by \( f{\left ( n \right )} \). Since we can think of the sequence as being enumerated, the notation \( a_{n} \) is employed for \( f{\left ( n \right )} \) where \( a \) is usually any choice of lower case alphabet characters like \( a , b , c , d , \ldots \). That said, we can notate the entire sequence by \( \left ( a_{n} \right ) \)