Definition 1: A constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object.[1]
Definition 2: Mathematical induction is a mathematical proof technique used to prove a given statement about any well-ordered set. Most commonly; it is used to establish statements for the set of natural numbers.[2]
Definition 3: Proof by contradiction is a form of proof, and more specifically a form of indirect proof, that establishes the truth or validity of a proposition. It starts by assuming that the opposite proposition is true, and then shows that such an assumption leads to a contradiction.[3]
Definition 4: A set is defined as numerable if all it’s elements are able to be counted or listed.
Canon 1: For finite sets counting the elements one by one demonstrates that the set is numerable. For infinite sets since all the elements are impossible to count, by definition, it is necessary to demonstrate that the elements of the set can, at least in theory, be listed with no exceptions. If in the process of listing the elements of an infinite set it is possible to demonstrate that at least one element will never appear in the list then the set is not numerable.
Definition 5: To enumerate a set is the process of listing the elements of the set.
Canon 2: Enumeration is an ordering process which proceeds from lowest to highest.
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