April 2018
Intermediate to advanced
408 pages
10h 42m
English
We can consider all numeric operations to be defined by recursions. For more details, read about the Peano axioms that define the essential features of numbers at: http://en.wikipedia.org/wiki/Peano_axioms.
From these axioms, we can see that addition is defined recursively using more primitive notions of the next number, or successor of a number, n,
.
To simplify the presentation, we'll assume that we can define a predecessor function,
, such that , as long as . This formalizes the idea that a number is the successor ...