Real Numbers

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 prime factors. For example, 6

The process of expressing a composite

The process of expressing a composite number as a product of prime numbers. Using factor trees, any number like 32760 can be written as 2³ × 3² × 5 ×

Numbers that cannot be expressed

Numbers that cannot be expressed in the form p/q where p and q are integers and q ≠ 0. Examples include √2, √3, √5, π, and non-terminating non-repeati

A mathematical technique where we assume

A mathematical technique where we assume the opposite of what we want to prove and show that this leads to a contradiction, thus proving our original

If a prime p divides a²

If a prime p divides a², then p must divide a. This property is derived from the Fundamental Theorem of Arithmetic.