**Description: **The natural numbers of
analysis start at one (unlike the ordinal natural
numbers, i.e. the members of the set , df-om 4875, which start at
zero). This is the convention used by most analysis books, and it is
often convenient in proofs because we don't have to worry about division
by zero. See nnind 10049 for the principle of mathematical induction.
See
dfnn2 10044 for a slight variant. See df-n0 10253 for the set of nonnegative
integers
starting at zero. See dfn2 10265 for defined in terms
of .
This is a technical definition that helps us avoid the Axiom of Infinity
in certain proofs. For a more conventional and intuitive definition
("the
smallest set of reals containing as well as the successor of every
member") see dfnn3 10045. (Contributed by NM,
10-Jan-1997.) |