2019-04-18T13:07:04+03:00[Europe/Moscow] en true Goldbach Conjecture, Infinity Many Primes, Square Root Irrationality, Ratio of Rational Numbers, Natural Numbers, Pigeonhole Principle, Fibonacci Sequence, Golden Ratio, Prime Numbers, Composite Numbers, Prime Factorization, Mersenne Primes, Theorem, Conjecture, Prime Gap, Number of Primes, Twin Prime Conjecture, One to One Correspondence, Infinite Natural Numbers, Cardinality, Rational Numbers, Irrational Numbers, Natural Numbers and Integers, Natural and Rational Numbers, Natural and Real numbers flashcards
Great Ideas in Mathematics

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"