Question

What are n-tuples?

Answer 1

To explore these ideas further, we start with some terminology and notation. The set of all real numbers can be viewed geometrically as a line. It is called the real line and is denoted by $R$ or $R^{1}$. The superscript reinforces the intuitive idea that a line is onedimensional. The set of all ordered pairs of real numbers (called 2-tuples) and the set of all ordered triples of real numbers (called 3-tuples) are denoted by $R^{2}$ and $R^{3}$, respectively. The superscript reinforces the idea that the ordered pairs correspond to points in the plane (two-dimensional) and ordered triples to points in space (three-dimensional). The following definition extends this idea.