Talk:Definition by Induction of Natural Number Addition

The text following "This can be expressed as:" is easier to read than the text before it. So what is the point of initial, more complicated definition?--TonyH (talk) 14:01, 29 September 2013 (UTC)


 * In order to prove this rigorously, it is important to demonstrate that there is a mapping which has the properties that are required. So as to do this, the language of mappings is employed. The more informal shorthand follows as it is subordinate to the intent of this theorem. --prime mover (talk) 15:14, 29 September 2013 (UTC)

Looking at the page again I see that it is a theorem. I thought this was the definition of addition of natural numbers. If this is a theorem, where is the definition then?--TonyH (talk) 14:10, 29 September 2013 (UTC)


 * The proof is demonstrating that the definition of addition as defined in the axiomatic specification of the naturally ordered semigroup is the same thing as that defined by the Peano axioms. I will take on board the fact that the links to the actual definitions themselves is less than perfect, and raise a note to get them improved. --prime mover (talk) 15:14, 29 September 2013 (UTC)