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Principia mathematica, vol. 1 (of 3)

*52. THE CARDINAL NUMBER 1.

Project Gutenberg EPUB3 edition Whitehead, Alfred North and Russell, Bertrand
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This proposition is frequently useful. We shall define the number 0 as ; thus the above proposition states that a class has one member or none when, and only when, all its members are identical. It will be seen that does not imply , and therefore allows the possibility of having no members.

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Principia mathematica, vol. 1 (of 3), Project Gutenberg eBook #78050

FOOTNOTES: *53. MISCELLANEOUS PROPOSITIONS INVOLVING UNIT CLASSES.