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# Real Number
Real numbers are all [numbers](number.md) found on the infinite, continuous one dimensional number line, they often represent what we generally just mean by the term "number" and include for example [zero](zero.md), [pi](pi.md) or -39/11. The [set](set.md) or real numbers includes all [whole numbers](integer.md) as well as all [rational numbers](rational_number.md) (fractions with integer nominator and denominator), but in addition contains infinitely many "special" numbers such as [pi](pi.md), [e](e.md) or [square root](sqrt.md) of 2, numbers that are mathematically very interesting because they for example produce infinitely many digits in our traditional number notation without showing any obvious patterns. However it has to be noted real numbers still do NOT include for example [infinity](infinity.md) or [complex numbers](complex_number.md) (kind of "2D extension" of real numbers) such as [i](i.md). Real numbers really represent a **[continuum](continous.md)**, between any two numbers that are not the same there is always infinitely many real numbers that have no gaps in between -- this leads to the fact that not only is there infinitely many real numbers, but there is **[uncountably many](uncountable.md)** of them, i.e. simply put there is "more than traditional infinity" of real numbers.
Real numbers are all [numbers](number.md) found on the infinite, continuous one dimensional number line, they often represent what we generally just mean by the term "number" and include for example [zero](zero.md), [pi](pi.md) or -39/11. The [set](set.md) or real numbers includes all [whole numbers](integer.md) as well as all [rational numbers](rational_number.md) (fractions with integer nominator and denominator), but in addition contains infinitely many "special" numbers such as [pi](pi.md), [e](e.md) or [square root](sqrt.md) of 2, numbers that are mathematically very interesting because they for example produce infinitely many digits in our traditional number notation without showing any obvious patterns. However it has to be noted real numbers still do NOT include for example [infinity](infinity.md) or [complex numbers](complex_number.md) (kind of "2D extension" of real numbers) such as [i](i.md). Real numbers really represent a **[continuum](continous.md)**, between any two numbers that are not the same there is always infinitely many real numbers that have no gaps in between -- this leads to the fact that not only is there infinitely many real numbers, but there is **[uncountably many](uncountable.md)** of them, i.e. simply put there is "more than traditional infinity" of real numbers. [Mathematically](math.md) the set of real numbers and operations with them form a structure called a *[field](field.md)* (so you'll often hear the term "field of real numbers").
WATCH OUT: even though in programming we sometimes we encounter [data types](data_type.md) named *real*, they usually don't represent true real numbers! In [programming](programming.md) we mostly only [approximate](approximation.md) real numbers with [floating](float.md) or [fixed](fixed_point.md) point numbers, which really are only rational numbers -- this is practically always [good enough](good_enough.md), we don't ever need an exact value of pi, a few decimal digits of accuracy is enough to an engineer, but to a mathematician real numbers represent a completely new, different world with some fundamental differences, which even a mere programmer should be at least aware of. Real numbers are tied to questions of the continuum, infinitely big and infinitely small, and they can really eventually lead to deep philosophical debates.