Discrete Mathematics Study Center
... Let P(x) denote "x is greater than 5", where the universe of discourse is the set of integers. Then the truth value of ∀x P(x) is F , since, for example, P(4) is F . Note that if the universe of discourse had been the set of all integers greater than or equal to 6, then ∀x P(x) would have truth valu ...
... Let P(x) denote "x is greater than 5", where the universe of discourse is the set of integers. Then the truth value of ∀x P(x) is F , since, for example, P(4) is F . Note that if the universe of discourse had been the set of all integers greater than or equal to 6, then ∀x P(x) would have truth valu ...
Fibonacci numbers
... The value 1+2 5 is the positive root of the equation x2 − x − 1 = 0 and is often referred to as α. It arises often enough in mathematics and has such interesting properties that we also frequently refer to it as the golden ratio. We will now apply this ratio to a few interesting geometric scenarios. ...
... The value 1+2 5 is the positive root of the equation x2 − x − 1 = 0 and is often referred to as α. It arises often enough in mathematics and has such interesting properties that we also frequently refer to it as the golden ratio. We will now apply this ratio to a few interesting geometric scenarios. ...
What is Zeckendorf`s Theorem?
... (ds . . . d2 d1 d0 )2 with each iteration, so the process must eventually terminate, as a number has only finitely many representations in radix-F . Hence, we will eventually have (Z1), (Z2), and (Z3), and thus, a Zeckendorf representation for n + 1. We may further generalize the addition of two num ...
... (ds . . . d2 d1 d0 )2 with each iteration, so the process must eventually terminate, as a number has only finitely many representations in radix-F . Hence, we will eventually have (Z1), (Z2), and (Z3), and thus, a Zeckendorf representation for n + 1. We may further generalize the addition of two num ...
Sequences of Numbers Involved in Unsolved Problems, Hexis, 1990, 2006
... also online, email: superseeker@research.att.com ( SUPERSEEKER by N. J. A. Sloane, S. Plouffe, B. Salvy, ATT Bell Labs, Murray Hill, NJ 07974, USA); N. J. A. Sloane, e-mails to R. Muller, February 13 - March 7, 1995. ...
... also online, email: superseeker@research.att.com ( SUPERSEEKER by N. J. A. Sloane, S. Plouffe, B. Salvy, ATT Bell Labs, Murray Hill, NJ 07974, USA); N. J. A. Sloane, e-mails to R. Muller, February 13 - March 7, 1995. ...
Collatz conjecture
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as wondrous numbers.Take any natural number n. If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process (which has been called ""Half Or Triple Plus One"", or HOTPO) indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. The property has also been called oneness.Paul Erdős said about the Collatz conjecture: ""Mathematics may not be ready for such problems."" He also offered $500 for its solution.