# Name

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
A linguistic expression to denote a specified object. The object denoted by a given name is called the denotation. In mathematics, names are widely used for specific mathematical objects, for example, $e , \pi$ for the well-known transcendental numbers, $\sin$ for the sine function, $\emptyset$ for the empty set. From such simple names one can form compound names, which name an object using the names of two objects. For example, $\sin \pi$ is another name for the number $0$. A name not only names the denotation, but it also expresses a definite meaning. Thus, the expressions
$$\lim\limits _ {n \rightarrow \infty } n ^ {1/n} \ \textrm{ and } \ \ \sin \frac \pi {2}$$
Along with names, one uses in mathematics expressions containing variables. The expressions become names upon replacing the variables by names of objects in the range of values of the variables. Such expressions are called name forms. The expressions $e ^ {x}$, $\int _ {0} ^ {x} ( \sin t ) d t / t$, where $x$ is a variable for the real numbers, are examples of name forms.