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_nxⁿ + a_n-1x^n-1 + a_n-2x^n-2 + ... + a₁x¹ + a₀ = 0, x , a₀,...,a_n }

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