Mod Function Discrete Math

From a night class at fordham university nyc fall 2008.

Mod function discrete math. Our solution will be x a 1 y 1 n 1 a k y k n k mod n to see why this works consider what values x mod m k takes. The modulo operation is to be distinguished from the symbol mod which refers to the modulus one is operating from. A function or mapping defined as f. X is called domain and y is called codomain of function f.

For example 3 3 but not 3. Identity of mod is like this example 3 3 x x. The mod function is categorized under excel math and trigonometry functions. We then set y i be the inverse of n i mod m i for all i so y i n i 1 mod m i.

In computing the modulo operation returns the remainder or signed remainder of a division after one number is divided by another. If a is not congruent to b modulo m we write a 6b mod m. A familiar use of modular arithmetic is in the 12 hour clock in which the day is divided into two 12. Cheat sheet study sheet for a discrete math class that covers sequences recursive formulas summation logic sets power sets functions combinatorics arrays and matrices.

Mod is a function in mathematics that change any negative number to positive numbar. In mathematics modular arithmetic is a system of arithmetic for integers where numbers wrap around when reaching a certain value called the modulus the modern approach to modular arithmetic was developed by carl friedrich gauss in his book disquisitiones arithmeticae published in 1801. We say that a b mod m is a congruence and that m is its modulus. Given two positive numbers a and n a modulo n is the remainder of the euclidean division of a by n where a is the dividend and n is the divisor.

Modulo for negative numbers may be defined differently for example x86 processors standard pc and newer macintoshes defines it like that a mod n a mod n but mathematicians most often define it by using division algorithm. Two integers are congruent mod m if and only if they have the same remainder when divided by m. We introduce modular arithmetic the function that outputs remainders and separates them into equivalence classes. For example the expression 5 mod 2 would evaluate to 1 because 5 divided by 2 has a quotient of 2 and.

R a mod b where a bq r 0 le r lt b q in mathbb z. It is also known as modules. Mod don t change any positive number to negative. The function helps find a remainder after a number known as dividend is divided by another number known as divisor.

Discrete math cheat sheet study sheet study guide in pdf. X y is a relationship from elements of one set x to elements of another set y x and y are non empty sets.