Types of Numbers
The numerals we use to represent numbers in the Western world
were originally from India before about 400CE.
Gradually these numerals were adopted by the Arab world, which also gave us
al-gorithms and al-gebra.
Sometimes numerals can be used in the same way as words, for
example in a soccer team a player might have a "3" on their shirt
or equally "left defender". A player with "9" on their shirt is not
necesarily 3 times better than the "3" player. The numerals are
basically names
and these are "nominal" numbers.
Nominal numbers can also be "ordinal" in that they imply an
order but nothing else.
The most important numbers are integers and are the counting numbers.
They are called "cardinal" which in this context means important.
Next we have fractions, written with a vinculum with numerator and denominator.
These are called "real" numbers. Those real numbers that
can be written as
numerator divided by denominator are ratios and are
called "rational" numbers.
Real numbers that cannot be written as ratios are called
"irrational". All of the square roots of non-square
numbers are irrational, i.e. \(\sqrt 2\), \(\sqrt 7\) and so on.
Two well known irrational numbers are \( \pi \)
and \(e\) (Euler's number).
The next type of number is called the opposite of "real", namely
"imaginary". Imaginary numbers involve the square root of -1.
In physics this is usually denoted by \(\pm i\) while engineers often
use \( \pm j \).
"Complex" numbers are a combination of a real and an imaginary number
and can be written as \(a + ib\).
The final two classes of numbers are based on whether they can be written
as the evaluation of an expression, "algebraic" or
"transcendental". The square root of 3 is irrational
and algebraic. \(\pi\) is irrational and transcendental.
Integers (cardinal numbers)
Reals (rational, irrational, algebraic, transcendental)
Imaginary (involve \( \sqrt -1\))
Complex (real + i real)
Some More Stuff
Dottie's number
Fibonacci Sequence
The Golden Ratio
\(\aleph_0\) Aleph Null
Kaprekar's Number
Armstrong Numbers
Friedman Numbers
and so on