## Now, since all the ξ's are bounded above, since {x n } is CS, we have a supremum for the non-empty set, {ξ 0 Let this supremum be x. I claim that this x has the property stated in the theorem

- Now, since all the ξ's are bounded above, since…

Peano’s Axioms. N is a set with the following properties. (1) N has a distinguished element which we call ‘1’. (2) There exists a distinguished set map σ : N→ N. (3) σ is one-to-one (injective). (4) There does not exist an element n ∈ N such that σ(n) = 1. (So, in particular σ is not surjective). (5) (Principle of Induction) Let S ⊂ N such that a) 1 ∈ S and… (More)

@inproceedings{Kumar2009ConstructionON,
title={Construction of Number Systems},
author={N. Mohan Kumar},
year={2009}
}