Mathematical FunctionsThe following are the functions which are widely used in computer science. 1. Floor Functions: The floor function for any real number x is defined as f (x) is the greatest integer 1 less than or equal to x. It is denoted by [x]. Example: Determine the value of (i)[3. 5] (ii)[2.4] (iii)[3. 143]. Solution: (i)[3 . 5] = 3 (ii) [2 .4] = 3 (iii) [3. 143] = 3 2. Ceiling Functions: The ceiling function for any real number x is defined as h (x) is the smallest integer greater than or equal to x. It is denoted by [x]. Example: Determine the value of (i)[3. 5] (ii) [2.4] (iii) [3. 143]. Solution: (i)[3. 5] = 4 (ii) [2 .4] = 2 (iii) [3. 143] = 4. 3. Remainder Functions: The integer remainder is obtained when some a is divided by m. It is denoted by a (MOD m). We can also define it as, a (MOD m) is the unique integer t such that a = Mq + t. Here q is quotient 0 ≤ r < M. Example: Determine the value of the following: (i) 35 (MOD 7) (ii) 20 (MOD 3) (iii) 4 (MOD 9) Solution: (i) 35 (MOD 7) = 0 (ii) 20 (MOD 3) = 2 (iii) 4 (MOD 9) = 4 4. Exponential Functions: Consider two sets A and B. Let A = B = I_{+} and also let f: A → B be defined by f (n) = k^{n}. Here n is a +ve integer. The function f is called the base k exponential function. Note1: k^{t}= k. k. k.......k (t times).
