9th Grade - types of numbers

1 - Types of numbers

Different types

Numbers can be classified into different sets. Here are the most useful sets:

is the set of natural numbers. They are numbers without point and greater than zero.
 are natural numbers. aren't natural numbers.

is the set of relative numbers, or integers. They are numbers without point.
 are integers. aren't integers.

is the set of decimal numbers. They are numbers with a finite number of figures after the point.
 are decimal numbers. aren't decimal numbers.

is the set of rational numbers. They are the numbers you can write in the form of fractions.
 are rational numbers. aren't rational numbers.

is the set of real numbers. Every number you know is a real number.

is the set of positive numbers.

is the set of negative numbers.

is the set of numbers but without zero.

The number -4 belongs to the set of relative numbers. You can also write : . The same way, , and
.

Intervals

[2;3] is the set of all numbers between 2 and 3.
[4;5[ is the set of all numbers between 4 and 5, except 5.
]-2;1[ is the set of all numbers between -2 and 1, except -2 and 1.

Union of sets

The union of two sets, is the set of numbers that belong to the first set added to the set of numbers that belong to the second set.
You symbolize the union by a capital u : U.
[1;2]U[4;5]
[0;4]U[2;5] = [0;5]
]-4;-2]U]-3;-1] = ]-4 ; -1]

Intersection of intervals

The intersection of two intervals is the set of the numbers that belong to the first and the second one.:

The last result is the empty set, that is the set without any number in it.

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Types of numbers

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