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:<math>b(x) = (x = y) </math>.
Traditionally, this definition was introduced by [[Alfred North Whitehead|Whitehead]] and [[Bertrand Russell|Russell]]<ref>{{cite book | first=Alfred North | last=Whitehead |author2=Bertrand Russell | year=1910 | title=[[Principia Mathematica (Russell-Whitehead)|Principia Mathematica]] | page=37 }}</ref> along with the definition of the [[1 (number)|natural number 1]], as
:<math>1 \ \overset{\underset{\mathrm{def}}{}}{=} \ \hat{\alpha}\{(\exists x) . \alpha = \iota \jmath x\}</math>, where <math>\iota \jmath x \ \overset{\underset{\mathrm{def}}{}}{=} \ \hat{y}(y = x)</math>.
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