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Definition df-ceil 9643
Description: The ceiling (least integer greater than or equal to) function. Defined in ISO 80000-2:2009(E) operation 2-9.18 and the "NIST Digital Library of Mathematical Functions" , front introduction, "Common Notations and Definitions" section at http://dlmf.nist.gov/front/introduction#Sx4. See ceilqval 9678 for its value, ceilqge 9682 and ceilqm1lt 9684 for its basic properties, and ceilqcl 9680 for its closure. For example,  ( `  (
3  /  2 ) )  =  2 while  ( `  -u ( 3  /  2
) )  =  -u
1 (ex-ceil 11310).

As described in df-fl 9642 most theorems are only for rationals, not reals.

The symbol ⌈ is inspired by the gamma shaped left bracket of the usual notation. (Contributed by David A. Wheeler, 19-May-2015.)

Assertion
Ref Expression
df-ceil  |- =  ( x  e.  RR  |->  -u ( |_ `  -u x
) )

Detailed syntax breakdown of Definition df-ceil
StepHypRef Expression
1 cceil 9641 . 2  class
2 vx . . 3  setvar  x
3 cr 7328 . . 3  class  RR
42cv 1288 . . . . . 6  class  x
54cneg 7633 . . . . 5  class  -u x
6 cfl 9640 . . . . 5  class  |_
75, 6cfv 5002 . . . 4  class  ( |_
`  -u x )
87cneg 7633 . . 3  class  -u ( |_ `  -u x )
92, 3, 8cmpt 3891 . 2  class  ( x  e.  RR  |->  -u ( |_ `  -u x ) )
101, 9wceq 1289 1  wff =  ( x  e.  RR  |->  -u ( |_ `  -u x
) )
Colors of variables: wff set class
This definition is referenced by:  ceilqval  9678
  Copyright terms: Public domain W3C validator