Real Numbers

For any two positive integers

For any two positive integers a and b, there exist unique integers q (quotient) and r (remainder) such that a = bq + r, where 0 ≤ r < b. This algorith

Every composite number can be expressed

Every composite number can be expressed as a product of primes, and this factorization is unique (except for the order of factors). Example: 60 = 2² ×

Using proof by contradiction

Using proof by contradiction: Assume √p is rational, then √p = a/b where a, b are integers with no common factor other than 1. This leads to p dividin

A rational number p/q has

A rational number p/q has: (1) Terminating decimal if q = 2ᵐ × 5ⁿ for some non-negative integers m, n. (2) Non-terminating repeating decimal if q has