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Explanation: 1.5: Comparing the Size of Sets and Their Subsets

(related to Subsection: Common Notions (all Books))

(Common Notion 5 from Book 1 of Euclid's “Elements”)

And the whole [is] greater than the part.

Modern Formulation (Proposal)1

The cardinality of a set is greater than the cardinality of its subset.

Mentioned in:

Proofs: 1 2 3

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Github:
bookofproofs
non-Github:
@Fitzpatrick

References

Adapted from (subject to copyright, with kind permission)

  1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"

Footnotes

  1. Today we know that this modern formulation is not true! It holds only for finite sets. In the time of Euclid, mathematicians and philosophers had only a vivid concept of "the whole" and "its part" which is totally different from contemporary set-theoretical concepts. ↩