# Number Theory/Irrational, Rational, Algebraic, And Transcendental Numbers

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**Rational** numbers can be expressed as the ratio of two integers **p** and **q** 0 expressed as **p/q**. In set notation: { **p/q**: **p**,**q** **q** 0 }

**Irrational** numbers are those real numbers contained in but not in , where denotes the set of real numbers. In set notation: { **x**: **x** , **x** }

**Algebraic** numbers, sometimes denoted by , are those numbers which are roots of an algebraic equation with integer coefficients (an equivalent formulation using rational coefficients exists). In math terms: { **x**: a_{n}x^{n} + a_{n-1}x^{n-1} + a_{n-2}x^{n-2} + ... + a_{1}x^{1} + a_{0} = 0, **x** , a_{0},...,a_{n} }

**Transcendental** numbers are those numbers which are **Real** () , but are not **Algebraic** (). In set notation: { **x**: **x** , **x** }