Gregory number
In mathematics, a Gregory number, named after James Gregory, is a real number of the form:[1]
where x is any rational number greater or equal to 1. Considering the power series expansion for arctangent, we have
Setting x = 1 gives the well-known Leibniz formula for pi. Thus, in particular,
is a Gregory number.
Properties
See also
References
- ^ Conway, John H.; R. K. Guy (1996). The Book of Numbers. New York: Copernicus Press. pp. 241–243.
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Real numbers
- 0.999...
- Absolute difference
- Cantor set
- Cantor–Dedekind axiom
- Completeness
- Construction
- Decidability of first-order theories
- Extended real number line
- Gregory number
- Irrational number
- Normal number
- Rational number
- Rational zeta series
- Real coordinate space
- Real line
- Tarski axiomatization
- Vitali set
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