Group Name Symbol
...,3,2,1, 0, 1, 2, 3... integers Z (after the German word Zahl,
for “number”)
1, 2, 3... positive integers Zor N
(or often referred to
as natural numbers)
1, 2, 3... negative integers Z
0, 1, 2, 3 ... nonnegative integers Z* (Z-star)
(or often referred to as
whole numbers)
0, 1, 2, 3 ... nonpositive integers (no symbol)What do integers include?
Integers include the whole numbers (also called positive integers or natural num-
bers), negative whole numbers (also called negative integers or the negatives of the
naturals), and zero. Numbers such as 3/4, 5.993, 6.2, 3.2, and pi (π; or 3.14 ...) are
notconsidered integers. Only integers are used when speaking of odd and even num-
bers (zero is considered to be an even number; for more about zero, see p. 90).What is a place value?
The place value,or “rule of position,” are numbers whose value depends on the place
or position they occupy in a written numerical expression. In the Hindu-Arabic count-
ing system, the numerals 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0 have certain specific place val-
ues. For example, the number 7 represents 7 (7 units), 70 (as 7 tens), 700 (as 7 hun-
dreds), and so on—the 7’s values based on their position in the numerical expression.
(For more information about place values, see “History of Mathematics.”)What are some of the highest numberswe know?
Numbers can go on forever—in other words, there is an infinite number of numbers.
The highest numbers we are most familiar with include million, billion, and trillion,
which we often see when referring to such quantities as the number of miles to the
outer planets or the federal budget deficit. These larger numbers are usually separated
by commas at the thousands, millions, trillions, etc., place values. For example, for
3,490 the comma is after the thousand place value; for 1,384,993 it is put after the
million and thousand place value. Larger numbers written for technical papers are
sometimes expressed with spaces; for example, 11 384 443 is equivalent to 11,384,443.
Not every country labels the highest numbers in the same way. For example, in
the American system denominations above 1,000 million (or the American billion) are
72 1,000 times the preceding one (for example, one trillion is 1,000 billion; one