Mathematical Proof - College of the Siskiyous | Home
... To do this, I will show that if I assume that the equation is true for n = k, I can prove that the equation is also true for n = k + 1. ...
... To do this, I will show that if I assume that the equation is true for n = k, I can prove that the equation is also true for n = k + 1. ...
REDUCTIO AD ABSURDUM* (Proof by contradiction) Y.K. Leong
... So far our examples are taken from very classical, if not ancient, mathematics. As a contrast, we give an example of proof by contradiction from mathematics of recent vintage - if one may consider one hundred years ago as recent enough. The subject itself has only been recently introduced to element ...
... So far our examples are taken from very classical, if not ancient, mathematics. As a contrast, we give an example of proof by contradiction from mathematics of recent vintage - if one may consider one hundred years ago as recent enough. The subject itself has only been recently introduced to element ...
Chapter 0 - Ravikumar - Sonoma State University
... • Assertions: Mathematical statement expresses some property of a set of defined objects. Assertions may or may not be true. ...
... • Assertions: Mathematical statement expresses some property of a set of defined objects. Assertions may or may not be true. ...
A Brief Note on Proofs in Pure Mathematics
... You should note that induction can only be applied when the statements are indexed by the natural numbers. There has to be a first case (the base case), and you have to have be able to move to the ‘next’ statement (the induction step). If the statements are indexed by real numbers, then there is no ...
... You should note that induction can only be applied when the statements are indexed by the natural numbers. There has to be a first case (the base case), and you have to have be able to move to the ‘next’ statement (the induction step). If the statements are indexed by real numbers, then there is no ...
Class Notes (Jan.30)
... Proofs • A theorem is a mathematical statement that can be shown to be true. • An axiom or postulate is an assumption accepted without proof. • A proof is a sequence of statements forming an argument that shows that a theorem is true. The premises of the argument are axioms and previously proved the ...
... Proofs • A theorem is a mathematical statement that can be shown to be true. • An axiom or postulate is an assumption accepted without proof. • A proof is a sequence of statements forming an argument that shows that a theorem is true. The premises of the argument are axioms and previously proved the ...
Mathematical proof
In mathematics, a proof is a deductive argument for a mathematical statement. In the argument, other previously established statements, such as theorems, can be used. In principle, a proof can be traced back to self-evident or assumed statements, known as axioms. Proofs are examples of deductive reasoning and are distinguished from inductive or empirical arguments; a proof must demonstrate that a statement is always true (occasionally by listing all possible cases and showing that it holds in each), rather than enumerate many confirmatory cases. An unproved proposition that is believed true is known as a conjecture.Proofs employ logic but usually include some amount of natural language which usually admits some ambiguity. In fact, the vast majority of proofs in written mathematics can be considered as applications of rigorous informal logic. Purely formal proofs, written in symbolic language instead of natural language, are considered in proof theory. The distinction between formal and informal proofs has led to much examination of current and historical mathematical practice, quasi-empiricism in mathematics, and so-called folk mathematics (in both senses of that term). The philosophy of mathematics is concerned with the role of language and logic in proofs, and mathematics as a language.