The whole numbers native 1 upwards. (Or native 0 upwards in some areas of mathematics). Read an ext ->

The set is 1,2,3,... Or 0,1,2,3,...

You are watching: Name the set(s) of numbers to which –5 belongs.


The totality numbers, 1,2,3,... An unfavorable whole number ..., -3,-2,-1 and also zero 0. So the set is ..., -3, -2, -1, 0, 1, 2, 3, ...


(Z is indigenous the German "Zahlen" meaning numbers, because I is used for the collection of imagine numbers). Read much more ->

Rational Numbers

The numbers you have the right to make by dividing one creature by another (but not splitting by zero). In other words fractions. Read much more ->

Q is for "quotient" (because R is used for the collection of real numbers).

Examples: 3/2 (=1.5), 8/4 (=2), 136/100 (=1.36), -1/1000 (=-0.001)

(Q is native the Italian "Quoziente" meaning Quotient, the result of dividing one number by another.)

Irrational Numbers

Any genuine number the is not a reasonable Number. Read much more ->


Algebraic Numbers

Any number the is a systems to a polynomial equation through rational coefficients.

Includes all Rational Numbers, and also some Irrational Numbers. Read much more ->

Transcendental Numbers

Any number that is not one Algebraic Number

Examples of transcendental numbers encompass π and e. Read more ->

Real Numbers

Any worth on the number line:

Can it is in positive, an unfavorable or zero.Can be reasonable or Irrational.Can it is in Algebraic or Transcendental.Can have actually infinite digits, such as 13 = 0.333...

Also see real Number Properties

They are called "Real" numbers since they space not imaginary Numbers. Read an ext ->


Imaginary Numbers

Numbers that once squared offer a an unfavorable result.

If girlfriend square a real number you always get a positive, or zero, result. For example 2×2=4, and (-2)×(-2)=4 also, therefore "imaginary" numbers deserve to seem impossible, yet they room still useful!

Examples: √(-9) (=3i), 6i, -5.2i

The "unit" imaginary number is √(-1) (the square source of minus one), and also its prize is i, or periodically j.

i2 = -1

Read much more ->

Complex Numbers

A combination of a real and an imagine number in the form a + bi, where a and also b are real, and also i is imaginary.

The values a and b have the right to be zero, for this reason the collection of genuine numbers and the set of imagine numbers are subsets that the set of complex numbers.

Examples: 1 + i, 2 - 6i, -5.2i, 4





Natural numbers space a subset that Integers

Integers space a subset of reasonable Numbers

Rational Numbers are a subset of the genuine Numbers

Combinations of Real and Imaginary numbers comprise the complicated Numbers.

Number sets In Use

Here space some algebraic equations, and the number collection needed to deal with them:

Equation equipment Number set Symbol
x − 3 = 0 x = 3 Natural number
x + 7 = 0 x = −7 Integers
4x − 1 = 0 x = ¼ Rational number
x2 − 2 = 0 x = ±√2 Real Numbers
x2 + 1 = 0 x = ±√(−1) Complex Numbers

Other Sets

We have the right to take an existing set symbol and also place in the optimal right corner:

a tiny + to average positive, or a tiny * to mean non zero, choose this:
Set of positive integers 1, 2, 3, ...
Set the nonzero integers ..., -3, -2, -1, 1, 2, 3, ...

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And us can always use set-builder notation.