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Goldbach Conjecture

Every number greater than 2 can be written as the sum of two primes

Infinity Many Primes

Let "m" be an arbitrary natural number

Square Root Irrationality

Proof by contradiction

Ratio of Rational Numbers

Take the length of the period and raise 10 to that power. Subtract the new number "N" by the original number, creating a fraction.

Natural Numbers

Set of numbers used for counting

Pigeonhole Principle

Objects > containers, one container will have at least two objects

Fibonacci Sequence

The next number in the sequence is the sum of the previous two. Every natural number is the sum of two Fibonacci numbers

Golden Ratio

Created with Fibonacci numbers, a fraction with ones continuing into infinity

Prime Numbers

Its only factors are one and itself

Composite Numbers

Has multiple factors

Prime Factorization

Factor tree to simplify a number to only prime numbers

Mersenne Primes

Very rare

Theorem

A statement that can be proven true

Conjecture

A statement that is thought to be true but cannot be proven

Prime Gap

The gap between primes increases in distance as you go towards infinity

Number of Primes

As "n" gets larger, the number of primes less than or equal to "n" approaching n/ln x n

Twin Prime Conjecture

There are infinitely many primes separated by only 2 numbers

One to One Correspondence

Two collections whose objects can be paired evenly (finite or infinite)

Infinite Natural Numbers

Assume set is finite

Cardinality

Number of objects in a set

Rational Numbers

Decimal expansion either ends or has a pattern

Irrational Numbers

Decimal expansion is infinite with no pattern

Natural Numbers and Integers

For ever even natural number, pair it with a positive integer

Natural and Rational Numbers

Use the square spiral to prove one-to-one correspondence

Natural and Real numbers

Build missing number "M"