Bracket Function : Number Theory #Bracket #Function #: #Number #Theory
Bracket Function : The function I : R → Z defined by I(x) = n where n ≤ x < n+1 is called the bracket function or the step function or the integral part function . Notation : Integral part of x in R is denoted by I(x) or [x]. Definition : If x 𝞊 R , x - [x] is called the Fractional part of x. Note : [x] ≤ x < [x] + 1 or x-1 < [x] ≤ x. For every x 𝞊 R, x ≥ [x] , hence the fractional part of x is always non-negative x 𝞊 Z ⇔ x=[x]. For example : * For 14/3 = 4.6666... , [ 14/3] = 4. * For 3/4, [3/4] = 0 because 0 < 3/4 < 1. * For π = 22/7 , we...