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.

Integers

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

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  ## Illustration

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, ...See more: You'Ll Never Guess What Does Darth Vader Mean In German, Darth Vader Doesn'T Mean Dark Father etc

And us can always use set-builder notation.