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Common systems of numbers:

Symbol Meaning Alternatives
𝔹 Boolean domain 𝔽2, β„€/2β„€
β„• Natural numbers (recommend including 0) β„•0, β„•0, β„€β‰₯0, β„€β‰₯, π•Ž
(without 0) β„•βˆ—, β„•+, β„•1, β„•>0, β„€+, β„€+, β„€>0, β„€>
β„€ Integers (from Zahlen)
β„™ Prime numbers
β„€/nβ„€ Integers modulo n β„€/(n), 𝔽p (when prime), GF(p) (when prime), β„€n (not recommended)
𝔽q Finite field GF(q), β„€/pβ„€ (when prime)
𝔽̅p Algebraic closure of finite field
𝔻 Dyadic rational numbers β„€[Β½]
β„€(p) Integers localized at p
β„š Rational numbers (from quoziente or β€œquotient”)
β„šΜ… Algebraic numbers 𝔸
ℝ Real numbers
𝕁 Irrational numbers β„βˆ’β„š, ℝ\β„š
𝕋 Circle group (or unit complex numbers, from β€œtorus”) ℝ/β„€, π•Š1, 𝕋1
β„‚ Complex numbers
ℍ Quaternions (from β€œHamilton”)
𝕆 Octonions
π•Š Sedenions
β„€p p-adic integers
β„€Μ‚ Profinite integers
β„šp p-adic numbers
𝔸℀ Integral adeles
π”Έβ„š,fin Finite adeles
π”Έβ„š Adeles
β„šΜ…p Algebraic p-adic numbers
β„‚p Complex p-adic numbers Ξ©p