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Sets of numbers

Numbers can be categorized in different sets of numbers.
The category the number belongs to, tells us what kind of number it is.

The most common sets of numbers

SymbolNameDescriptionExamples

\mathbb{N}


Natural numbers

All positive whole numbers.

1, 2, 3, 4, ....

\mathbb{N}_0

Natural numbers
with zerro

All positive whole numbers including zero.

0, 1, 2, 3, 4, ....

\mathbb{Z}


Integers

All whole numbers, positive and negative, including zero.
That is, number that can be written without use of fractions
or decimals.

..... -3, -2, -1, 0, 1,
2, 3, ....

\mathbb{Q}


Rational numbers

frac{a}{b}
All integers including zero or all numbers expressed as
fractions of two integers, the denominator of which is
not zero.


5

10

frac{2}{3}

frac{4}{5}


\mathbb{Q}'

Irrational numbers

All numbers that cannot be expressed as a simple fraction
or decimal number.

sqrt{2}

pi

All square roots
of primes.

\mathbb{R}

Real numbers

All sets of numbers above are contained in the set of
real numbers. So it is all positive and negative whole
numbers, zero, fractions, decimal numbers, square roots
or pi.

5

10.23

3.1415926535... (Pi)

sqrt{2}