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Definition df-sgn 12920
Description: Signum function. Pronounced "signum" , otherwise it might be confused with "sine". Defined as "sgn" in ISO 80000-2:2009(E) operation 2-9.13. It is named "sign" (with the same definition) in the "NIST Digital Library of Mathematical Functions" , front introduction, "Common Notations and Definitions" section at http://dlmf.nist.gov/front/introduction#Sx4. We define this over (df-xr 9653) instead of so that it can accept and . Note that df-psgn 16516 defines the sign of a permutation, which is different. Value shown in sgnval 12921. (Contributed by David A. Wheeler, 15-May-2015.)
Assertion
Ref Expression
df-sgn

Detailed syntax breakdown of Definition df-sgn
StepHypRef Expression
1 csgn 12919 . 2
2 vx . . 3
3 cxr 9648 . . 3
42cv 1394 . . . . 5
5 cc0 9513 . . . . 5
64, 5wceq 1395 . . . 4
7 clt 9649 . . . . . 6
84, 5, 7wbr 4452 . . . . 5
9 c1 9514 . . . . . 6
109cneg 9829 . . . . 5
118, 10, 9cif 3941 . . . 4
126, 5, 11cif 3941 . . 3
132, 3, 12cmpt 4510 . 2
141, 13wceq 1395 1
Colors of variables: wff setvar class
This definition is referenced by:  sgnval  12921
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