Editing Singleton (mathematics) (section)

==Definition in ''Principia Mathematica''==
The following definition was introduced in [[Principia Mathematica]] 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]]|volume=I | page=37 }}</ref> 
:<math>\iota</math>'''‘'''<math>x = \hat{y}(y = x)</math> '''Df.'''
The symbol <math>\iota</math>'''‘'''<math>x</math> denotes the singleton <math>\{x\}</math> and <math>\hat{y}(y = x)</math> denotes the class of objects identical with <math>x</math> aka <math>\{y : y=x\}</math>.  
This occurs as a definition in the introduction, which, in places, simplifies the argument in the main text, where it occurs as proposition 51.01 (p.&nbsp;357 ibid.).
The proposition is subsequently used to define the [[cardinal number]] 1 as
:<math>1=\hat{\alpha}((\exists x)\alpha=\iota</math>'''‘'''<math>x)</math> '''Df.'''  
That is, 1 is the class of singletons. This is definition 52.01 (p.&nbsp;363 ibid.)