Level 73
Level 74

Great Ideas in Mathematics


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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"
Level 75