Ordered triple in the context of Graph of a function of two variables

⭐ Core Definition: Ordered triple

In mathematics, a tuple is a finite sequence or ordered list of numbers or, more generally, mathematical objects, which are called the elements of the tuple. An $n$ -tuple is a tuple of $n$ elements, where $n$ is a non-negative integer. There is only one 0-tuple, called the empty tuple. A 1-tuple and a 2-tuple are commonly called a singleton and an ordered pair, respectively. The term "infinite tuple" is occasionally used for "infinite sequences".

Tuples are usually written by listing the elements within parentheses " $( )$ " and separated by commas; for example, $(2, 7, 4, 1, 7)$ denotes a 5-tuple. Other types of brackets are sometimes used, although they may have a different meaning.

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Ordered triple in the context of Graph of a function

In mathematics, the graph of a function $f$ is the set of ordered pairs $(x,y)$ , where $f(x)=y.$ In the common case where $x$ and $f(x)$ are real numbers, these pairs are Cartesian coordinates of points in a plane and often form a curve.The graphical representation of the graph of a function is also known as a plot.

In the case of functions of two variables – that is, functions whose domain consists of pairs $(x,y)$ –, the graph usually refers to the set of ordered triples $(x,y,z)$ where $f(x,y)=z$ . This is a subset of three-dimensional space; for a continuous real-valued function of two real variables, its graph forms a surface, which can be visualized as a surface plot.