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Definition df-o1 12909
Description: Define the set of eventually bounded functions. We don't bother to build the full conception of big-O notation, because we can represent any big-O in terms of and division, and any little-O in terms of a limit and division. We could also use limsup for this, but it only works on integer sequences, while this will work for real sequences or integer sequences. (Contributed by Mario Carneiro, 15-Sep-2014.)
Assertion
Ref Expression
df-o1
Distinct variable group:   , , ,

Detailed syntax breakdown of Definition df-o1
StepHypRef Expression
1 co1 12905 . 2
2 vy . . . . . . . . . 10
32cv 1686 . . . . . . . . 9
4 vf . . . . . . . . . 10
54cv 1686 . . . . . . . . 9
63, 5cfv 5390 . . . . . . . 8
7 cabs 12664 . . . . . . . 8
86, 7cfv 5390 . . . . . . 7
9 vm . . . . . . . 8
109cv 1686 . . . . . . 7
11 cle 9365 . . . . . . 7
128, 10, 11wbr 4267 . . . . . 6
135cdm 4811 . . . . . . 7
14 vx . . . . . . . . 9
1514cv 1686 . . . . . . . 8
16 cpnf 9361 . . . . . . . 8
17 cico 11247 . . . . . . . 8
1815, 16, 17co 6061 . . . . . . 7
1913, 18cin 3304 . . . . . 6
2012, 2, 19wral 2694 . . . . 5
21 cr 9227 . . . . 5
2220, 9, 21wrex 2695 . . . 4
2322, 14, 21wrex 2695 . . 3
24 cc 9226 . . . 4
25 cpm 7176 . . . 4
2624, 21, 25co 6061 . . 3
2723, 4, 26crab 2698 . 2
281, 27wceq 1687 1
Colors of variables: wff setvar class
This definition is referenced by:  elo1  12945
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