Proof: By Euclid
(related to Proposition: 7.32: Natural Number is Prime or has Prime Factor)
- In fact, if $A$ is prime then that which was prescribed has happened.
- And if (it is) composite then some prime number will measure it [Prop. 7.31].
- Thus, every number is either prime or is measured by some prime number.
- (Which is) the very thing it was required to show.
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References
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"
