The whole numbers from 1 upwards. (Or from 0 upwards in some fields of mathematics). Read More ->
The set is 1,2,3,... Or 0,1,2,3,...
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The whole numbers, 1,2,3,... Negative whole numbers ..., -3,-2,-1 & zero 0. So the phối is ..., -3, -2, -1, 0, 1, 2, 3, ...
(Z is from the German "Zahlen" meaning numbers, because I is used for the mix of imaginary numbers). Read More ->
The numbers you can make by dividing one integer by another (but not dividing by zero). In other words fractions. Read More ->
Q is for "quotient" (because R is used for the phối of real numbers).
Examples: 3/2 (=1.5), 8/4 (=2), 136/100 (=1.36), -1/1000 (=-0.001)
(Q is from the Italian "Quoziente" meaning Quotient, the result of dividing one number by another.)
Any real number that is not a Rational Number. Read More ->
Any number that is a solution lớn a polynomial equation with rational coefficients.
Includes all Rational Numbers, và some Irrational Numbers. Read More ->
Any number that is not an Algebraic Number
Examples of transcendental numbers include π & e. Read More ->
Any value on the number line:
Also see Real Number Properties
They are called "Real" numbers because they are not Imaginary Numbers. Read More ->
Numbers that when squared give a negative result.
If you square a real number you always get a positive, or zero, result. For example 2×2=4, & (-2)×(-2)=4 also, so "imaginary" numbers can seem impossible, but they are still useful!
Examples: √(-9) (=3i), 6i, -5.2i
The "unit" imaginary numbers is √(-1) (the square root of minus one), & its symbol is i, or sometimes j.
i2 = -1
Read More ->
A combination of a real and an imaginary number in the khung a + bi, where a and b are real, and i is imaginary.
The values a & b can be zero, so the set of real numbers và the set of imaginary numbers are subsets of the mix of complex numbers.
Examples: 1 + i, 2 - 6i, -5.2i, 4
Read More ->
Natural numbers are a subset of Integers
Integers are a subset of Rational Numbers
Rational Numbers are a subset of the Real Numbers
Combinations of Real & Imaginary numbers biến hóa the Complex Numbers.
Number Sets In Use
Here are some algebraic equations, and the number set needed lớn solve them:
|x − 3 = 0||x = 3||Natural Numbers|
|x + 7 = 0||x = −7||Integers|
|4x − 1 = 0||x = ¼||Rational Numbers|
|x2 − 2 = 0||x = ±√2||Real Numbers|
|x2 + 1 = 0||x = ±√(−1)||Complex Numbers|
We can take an existing phối symbol and place in the top right corner:a little + khổng lồ mean positive, or a little * to lớn mean non zero, lượt thích 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 always use set-builder notation.