Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-limsup Unicode version

Definition df-limsup 13294
 Description: Define the superior limit of an infinite sequence of extended real numbers. Definition 12-4.1 of [Gleason] p. 175. See limsupval 13297 for its value. (Contributed by NM, 26-Oct-2005.)
Assertion
Ref Expression
df-limsup
Distinct variable group:   ,

Detailed syntax breakdown of Definition df-limsup
StepHypRef Expression
1 clsp 13293 . 2
2 vx . . 3
3 cvv 3109 . . 3
4 vk . . . . . 6
5 cr 9512 . . . . . 6
62cv 1394 . . . . . . . . 9
74cv 1394 . . . . . . . . . 10
8 cpnf 9646 . . . . . . . . . 10
9 cico 11560 . . . . . . . . . 10
107, 8, 9co 6296 . . . . . . . . 9
116, 10cima 5007 . . . . . . . 8
12 cxr 9648 . . . . . . . 8
1311, 12cin 3474 . . . . . . 7
14 clt 9649 . . . . . . 7
1513, 12, 14csup 7920 . . . . . 6
164, 5, 15cmpt 4510 . . . . 5
1716crn 5005 . . . 4
1814ccnv 5003 . . . 4
1917, 12, 18csup 7920 . . 3
202, 3, 19cmpt 4510 . 2
211, 20wceq 1395 1
 Colors of variables: wff setvar class This definition is referenced by:  limsupcl  13296  limsupval  13297
 Copyright terms: Public domain W3C validator