Types of Numbers
There are a lot of different types of numbers
in the world. Each number is different than
another, yet they may share some common
characteristics. To help themselves keep track
of and understand the similarities and
differences between numbers, mathematicians
have developed a grouping system that
categorizes and describes numbers based on
their characteristics.
Some of the most common groups in the
system are:
Natural numbers
Whole numbers
Integers
Rationals
Real numbers
The grouping system is very similar to the
concept of grouping in geography in which
things are grouped in categories using
characteristics that get more and more
specific. (Country, state, county, city, street?)
What are Integers?
Integers are a special group or category of
numbers that:
Consist of the set of numbers: {?-4, -3, -2,
-1, 0, 1, 2, 3, 4?}
Are all positive and negative whole
numbers, which do not include any
fractional or decimal part.
A few things to note here:
1. There are no fractions or decimals in
any part of the numbers
2. Negative numbers often represent the
idea of being below a standard value.
3. Zero is an integer. In many other
number groups whether or not zero is
included makes a difference. Note that
zero is included in the set of integers.
4. Remember that categories of numbers
overlap. Just like categories of
geography (ex. country, state, county,
city, street) overlap each other (a street
is in a certain city, which is in a certain
county, which is in a certain state, etc.)
categories of math overlap each other
too.
5. Don't let the notation throw you off.
The brackets ( { } )are used to write
sets. This is the standard mathematical
notation used when you want to list a
group (or a 'set') of numbers. The
ellipse ( ? ) just means they go on and
on forever in the same pattern. This is
especially helpful when the group you
are trying to represent is too big to
write out in its entirety.
Examples
Examples of Integers:
The number of coins someone adds to or
removes from a jar. If you add three coins
to a jar, that would be represented by a
positive value: +3. Removing three coins
from a jar would be represented by a
negative value: -3. Since you can only add
or remove an entire coin from a jar (not
half of or a third of a coin) integers would
always represent the number of coins added
or taken.
Altitude, rounded to the nearest foot.
Denver is at an altitude of 5,183 ft. Parts of
New Orleans are at an altitude of -3 ft.
Temperature, rounded to the nearest degree
Celsius. Room temperature is approximately
22 degrees Celsius. Freezing is any value
below zero, -3 degrees Celsius for example.
Natural numbers. All natural numbers are
also integers. Since natural numbers are
the set of numbers {1, 2, 3, 4...} they are
also included in the set of integers.
Whole numbers. All whole numbers are also
integers. Since whole numbers are the set
of numbers {0, 1, 2, 3...} they are also part
of the set of integers. |
