How else is the term function used?
Unfortunately (as with many mathemati-
cal terms), there is often more than one
function for the word “function.” For
example, contrary to the definition above,
function can also mean the relationships
that map single points in the domain to
multiple points in the range—called mul-
tivalued functions—which is mainly used
in the theory of complex functions. To
further confuse matters, there are also
functions called non-multivalued func-
tions.
Where did the symbolfor infinity
originate?
Infinity is represented by the symbol , a
sign introduced by John Wallis in 1655 in
his treatise “De sectionibus conicus.”
Historians believe that Wallis, a classical scholar, adopted the sign from the late-
Roman symbol for “1,000.” Whether it was from there or another source, the result
was (and remains) the same: “a figure-eight on its side,” as many people describe the
infinity symbol.
Are there different types of infinity
in mathematics?
To most of us, the universe represents infinity, but in mathematics it is the unbound-
ed quantity that is greater than every real number. Called potential infinityin mathe-
matics, it is the potential for infinity that exists with natural numbers because one can
always conceive of a number greater than any given number. Another type of infinity
in mathematics is completed infinity,which refers to the size of an infinite set (such
as all the points on a line). At the end of the 19th century, German mathematician
George (Georg) Ferdinand Ludwig Philipp Cantor (1845–1918) showed that different
orders of infinity existed and that the infinity of points on a line was of a greater order
than that of prime numbers.
129
FOUNDATIONS OF MATHEMATICS
The expanses of the universe seem infinite to us, but
in mathematics the concept of infinity reaches even
beyond the edges of the universe toward numbers
that are inconceivably large. The Image Bank/Getty
Images.