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Definition df-nn 9957
 Description: The natural numbers of analysis start at one (unlike the ordinal natural numbers, i.e. the members of the set , df-om 4805, 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 9974 for the principle of mathematical induction. See dfnn2 9969 for a slight variant. See df-n0 10178 for the set of nonnegative integers starting at zero. See dfn2 10190 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 9970. (Contributed by NM, 10-Jan-1997.)
Assertion
Ref Expression
df-nn

Detailed syntax breakdown of Definition df-nn
StepHypRef Expression
1 cn 9956 . 2
2 vx . . . . 5
3 cvv 2916 . . . . 5
42cv 1648 . . . . . 6
5 c1 8947 . . . . . 6
6 caddc 8949 . . . . . 6
74, 5, 6co 6040 . . . . 5
82, 3, 7cmpt 4226 . . . 4
98, 5crdg 6626 . . 3
10 com 4804 . . 3
119, 10cima 4840 . 2
121, 11wceq 1649 1
 Colors of variables: wff set class This definition is referenced by:  nnexALT  9958  peano5nni  9959  1nn  9967  peano2nn  9968
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