Common Number Sets
There are sets of numbers
that are used so often that they have special names and symbols:
Symbol
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Description
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Natural Numbers
The set is {1,2,3,...} or {0,1,2,3,...}
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Integers
The whole numbers, {1,2,3,...} negative whole numbers
{..., -3,-2,-1} and zero {0}. So the set is {..., -3, -2, -1, 0, 1, 2, 3,
...}
(Z is for the German "Zahlen",
meaning numbers, because I is used for the set of imaginary
numbers). Read More ->
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Rational Numbers
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 set of
real numbers).
Examples: 3/2 (=1.5), 8/4 (=2),
136/100 (=1.36), -1/1000 (=-0.001)
(Q is for the Italian "Quoziente"
meaning Quotient, the result of dividing one number by another.)
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Irrational Numbers
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Algebraic Numbers
Any number that is a solution to a polynomial equation
with rational coefficients.
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Transcendental Numbers
Any number that is not an Algebraic
Number
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Real Numbers
All Rational and Irrational numbers. They can also be
positive, negative or zero.
Includes the Algebraic Numbers and Transcendental Numbers.
A simple way to think about the Real Numbers is: any
point anywhere on the number line (not just the whole
numbers).
Examples: 1.5, -12.3, 99,
√2, π
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Imaginary Numbers
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, and (-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), and its symbol is i, or
sometimes j.
i2 = -1
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Complex Numbers
A combination of a real and an imaginary number in the
form a + bi, where a andb are real,
and i is imaginary.
The values a and b can
be zero, so the set of real numbers and the set of imaginary numbers are
subsets of the set of complex numbers.
Examples: 1 + i, 2 - 6i,
-5.2i, 4
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Illustration
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 and Imaginary numbers make up the Complex Numbers.
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