The totality numbers from 1 upwards. (Or native 0 upwards in some fields of mathematics). Read more ->

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

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The entirety numbers, 1,2,3,... Negative whole numbers ..., -3,-2,-1 and zero 0. So the collection is ..., -3, -2, -1, 0, 1, 2, 3, ...


(Z is indigenous the German "Zahlen" an interpretation numbers, due to the fact that I is used for the collection of imagine numbers). Read more ->

Rational Numbers

The numbers you deserve to make by separating one essence by one more (but not dividing by zero). In various other words fractions. Read an ext ->

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

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

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

Irrational Numbers

Any real number the is not a reasonable Number. Read an ext ->


Algebraic Numbers

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

Includes every Rational Numbers, and some Irrational Numbers. Read an ext ->

Transcendental Numbers

Any number the is not an Algebraic Number

Examples that transcendental numbers incorporate π and also e. Read much more ->

Real Numbers

Any worth on the number line:

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

Also see real Number Properties

They are referred to as "Real" numbers since they space not imaginary Numbers. Read much more ->


Imaginary Numbers

Numbers that as soon as squared provide a an adverse result.

If friend square a genuine number you always get a positive, or zero, result. For instance 2×2=4, and (-2)×(-2)=4 also, for this reason "imaginary" numbers have the right to seem impossible, but 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 symbol is i, or periodically j.

i2 = -1

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Complex Numbers

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

The worths a and b have the right to be zero, so the set of real numbers and the set of imaginary numbers space subsets that the collection of complex numbers.

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





Natural numbers are a subset the Integers

Integers room a subset of rational Numbers

Rational Numbers are a subset that the real Numbers

Combinations that Real and also Imaginary numbers make up the complicated Numbers.

Number set In Use

Here space some algebraic equations, and also the number set needed to resolve them:

Equation equipment Number collection 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 can take an existing collection symbol and also place in the peak right corner:

a little + to median positive, or a small * to typical non zero, like this:
Set of positive integers 1, 2, 3, ...
Set of nonzero integers ..., -3, -2, -1, 1, 2, 3, ...

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And we can constantly use set-builder notation.