The Model Theory Of Dedekind Algebras ABSTRACT: A Dedekind algebra is an ordered pair (B, h) where B is a non-empty set and h is a "similarity transformation" on B. Among the Dedekind algebras is the sequence of positive integers. Each Dedekind algebra can be decomposed into a family of disjointed, countable subalgebras which are called the configurations of the algebra. There are many isomorphic types of configurations. Each Dedekind algebra is associated with a cardinal value function called
uclid’s proof of the Infinitude of Primes — Proof by contradiction (Reductio ad absurdum): (1.3.3) Prove that there are infinite number of prime numbers. Assume that there are finite many primes: T = {P1, P2, P3, P4, P5, P6… Pn} Let Q be a number which is equivalent to the product of the finite many prime numbers, plus one. Q = (P1 x P2 x P3 x P4 x P5… Pn) + 1 Therefore, there can only be two possible types of numbers that Q can be, namely a prime number, or a composite number. If Q is a prime