As an example, here are two of the Peano postulates:
For every natural number n, there exists another natural number S(n) called the successor of n
If n is a natural number and n = S(m), then m is the only x satisfying n = S(x)
By whatever may decree it, do I need to add to postulate 2 that m and x are natural numbers even though S(n) is only defined for natural numbers n?
As another example consider this definition of an injection:
We say that f is injective if for every x and y in the domain of f, f(x) = f(y) implies x = y.
Need I specify that f is a function if I haven't defined the domain of any other object? Is it assumed that we shall never speak of nonsensical things like the domain of a real number so that it's clear that f must be a function?
[link] [comments]
from math https://ift.tt/348Kd7v
Post a Comment