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

Definition df-ceil 12015
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 ceilval 12053 for its value, ceilge 12059 and ceilm1lt 12061 for its basic properties, and ceilcl 12057 for its closure. For example,  ( `  (
3  /  2 ) )  =  2 while  ( `  -u ( 3  /  2
) )  =  -u
1.

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 12013 . 2  class
2 vx . . 3  setvar  x
3 cr 9527 . . 3  class  RR
42cv 1436 . . . . . 6  class  x
54cneg 9850 . . . . 5  class  -u x
6 cfl 12012 . . . . 5  class  |_
75, 6cfv 5592 . . . 4  class  ( |_
`  -u x )
87cneg 9850 . . 3  class  -u ( |_ `  -u x )
92, 3, 8cmpt 4475 . 2  class  ( x  e.  RR  |->  -u ( |_ `  -u x ) )
101, 9wceq 1437 1  wff =  ( x  e.  RR  |->  -u ( |_ `  -u x
) )
Colors of variables: wff setvar class
This definition is referenced by:  ceilval  12053  dfceil2  12054
  Copyright terms: Public domain W3C validator