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Ceiling function. In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor (x). Similarly, the ceiling function maps x to the smallest integer greater than or equal to x, denoted ⌈x⌉ or ceil (x). [ 1]
In number theory, Euler's totient function counts the positive integers up to a given integer n that are relatively prime to n. It is written using the Greek letter phi as or , and may also be called Euler's phi function. In other words, it is the number of integers k in the range 1 ≤ k ≤ n for which the greatest common divisor gcd (n, k ...
Greatest common divisor. In mathematics, the greatest common divisor ( GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted . For example, the GCD of 8 and 12 is 4, that is, gcd (8, 12) = 4. [ 1][ 2]
The Collatz conjecture states that all paths eventually lead to 1. The Collatz conjecture[ a] is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1.
In number theory, the partition function p(n) represents the number of possible partitions of a non-negative integer n. For instance, p(4) = 5 because the integer 4 has the five partitions 1 + 1 + 1 + 1, 1 + 1 + 2, 1 + 3, 2 + 2, and 4 . No closed-form expression for the partition function is known, but it has both asymptotic expansions that ...
In mathematics, an integer-valued function is a function whose values are integers. In other words, it is a function that assigns an integer to each member of its domain . The floor and ceiling functions are examples of integer-valued functions of a real variable, but on real numbers and, generally, on (non-disconnected) topological spaces ...
A highly composite number is a positive integer that has more divisors than any smaller positive integer. A related concept is that of a largely composite number, a positive integer that has at least as many divisors as any smaller positive integer. The name can be somewhat misleading, as the first two highly composite numbers (1 and 2) are not ...
Power supply. four AAA alkaline batteries. Weight. 213 grams. Graphic calculators made by Casio include the touchscreen ClassPad 300 as well as the models with traditional buttons which can be divided into two main generations listed below. Casio produced the world's first graphing calculator, the fx-7000G .