Profinite integer
In mathematics, a profinite integer is an element of the ring (sometimes pronounced as zee-hat or zed-hat) Z ^ = lim ← Z / n Z , {\displaystyle {\widehat {\mathbb {Z} }}=\varprojlim \mathbb {Z} /n\mathbb {Z} ,} where the inverse limit of the quotient rings Z / n Z {\displaystyle \mathbb {Z} /n\mathbb {Z} } runs through all natural numbers n {\displaystyle n} , partially ordered by divisibility. By definition, this ring is the profinite completion of the integers Z {\displaystyle \mathbb {Z} } .