1. Prove: If the average of n numbers x , x
... 1. Prove: If the average of n numbers x1 , x2 , . . . , xn is A, then at least one of the numbers is greater than or equal to A. ...
... 1. Prove: If the average of n numbers x1 , x2 , . . . , xn is A, then at least one of the numbers is greater than or equal to A. ...
Example Proofs
... An integer n is even if and only if there exists another integer r such that n = 2*r. An integer n is odd if and only if there exists another integer r such that n = (2*r) + 1 If y | x, which is read as “x is divisible by y”, or “y divides evenly into x”, then x = yc, for some integer c. Remember in ...
... An integer n is even if and only if there exists another integer r such that n = 2*r. An integer n is odd if and only if there exists another integer r such that n = (2*r) + 1 If y | x, which is read as “x is divisible by y”, or “y divides evenly into x”, then x = yc, for some integer c. Remember in ...
a proof for goldbach`s conjecture
... the sum of two primes. In 1930, Lev Schnirelmann proved that every even number n ≥ 4 can be written as the sum of at most 20 primes. This result was subsequently enhanced by many authors; currently, the best known result is due to Olivier Ramar, who in 1995 showed that every even number n ≥ 4 is in ...
... the sum of two primes. In 1930, Lev Schnirelmann proved that every even number n ≥ 4 can be written as the sum of at most 20 primes. This result was subsequently enhanced by many authors; currently, the best known result is due to Olivier Ramar, who in 1995 showed that every even number n ≥ 4 is in ...
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.