MathItems

By a sequence, we mean a function $f$ defined on the set $J$ of all positive integers.

If $f(n)=x_n$, for $n\in J$, it is customary to denote the sequence $f$ by the symbol $\{x_n\}$, or sometimes by $x_1,x_2,x_3,\ldots$.

The values of $f$, that is, the elements $x_n$, are called the terms of the sequence.

If $A$ is a set and if $x_n\in A$ for all $n\in J$, then $\{x_n\}$ is said to be a sequence in $A$, or a sequence of elements of $A$.