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Definition df-o1 13313
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 13309 . 2
2 vy . . . . . . . . . 10
32cv 1394 . . . . . . . . 9
4 vf . . . . . . . . . 10
54cv 1394 . . . . . . . . 9
63, 5cfv 5593 . . . . . . . 8
7 cabs 13067 . . . . . . . 8
86, 7cfv 5593 . . . . . . 7
9 vm . . . . . . . 8
109cv 1394 . . . . . . 7
11 cle 9650 . . . . . . 7
128, 10, 11wbr 4452 . . . . . 6
135cdm 5004 . . . . . . 7
14 vx . . . . . . . . 9
1514cv 1394 . . . . . . . 8
16 cpnf 9646 . . . . . . . 8
17 cico 11560 . . . . . . . 8
1815, 16, 17co 6296 . . . . . . 7
1913, 18cin 3474 . . . . . 6
2012, 2, 19wral 2807 . . . . 5
21 cr 9512 . . . . 5
2220, 9, 21wrex 2808 . . . 4
2322, 14, 21wrex 2808 . . 3
24 cc 9511 . . . 4
25 cpm 7440 . . . 4
2624, 21, 25co 6296 . . 3
2723, 4, 26crab 2811 . 2
281, 27wceq 1395 1
Colors of variables: wff setvar class
This definition is referenced by:  elo1  13349
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