CHAPTER 1
... In proof by contradiction (also known a reduction ad absurdum, Latin for “by reduction toward the absurd”). It is shown that if some statement were so, logical contradiction occurs, hence the statement must be not so. This method is perhaps the most prevalent of mathematical proofs. A famous example ...
... In proof by contradiction (also known a reduction ad absurdum, Latin for “by reduction toward the absurd”). It is shown that if some statement were so, logical contradiction occurs, hence the statement must be not so. This method is perhaps the most prevalent of mathematical proofs. A famous example ...
PROOFS Math 174 May 2017 I. Introduction. In the natural sciences
... of algebra, or facts about whole numbers, or other statements we’ve proven true—and arrive at the fact that q is true. Here’s an example. Theorem. If n is an even integer, then so is n2 . This is a p → q statement where p is the statement that n is some even integer and q is the statement that n2 is ...
... of algebra, or facts about whole numbers, or other statements we’ve proven true—and arrive at the fact that q is true. Here’s an example. Theorem. If n is an even integer, then so is n2 . This is a p → q statement where p is the statement that n is some even integer and q is the statement that n2 is ...
Quiz Game Midterm
... Let’s do a proof by cases on premise 3. Case 1: Assume that A. From this and premise 1, B follows by modus ponens. Case 2: Assume that C. This is equivalent to C by double negation. From this and premise 2, B follows by modus tollens. But by double negation, this is just B. So either way B follo ...
... Let’s do a proof by cases on premise 3. Case 1: Assume that A. From this and premise 1, B follows by modus ponens. Case 2: Assume that C. This is equivalent to C by double negation. From this and premise 2, B follows by modus tollens. But by double negation, this is just B. So either way B follo ...
On the Interpretation of Intuitionistic Logic
... That the second problem is different from the first is clear, and makes no special intuitionistic claim3 . The fourth and fifth problems are examples of conventional problems; while the presupposition of the fifth problem is impossible, and as a consequence the problem is itself content-free. The pr ...
... That the second problem is different from the first is clear, and makes no special intuitionistic claim3 . The fourth and fifth problems are examples of conventional problems; while the presupposition of the fifth problem is impossible, and as a consequence the problem is itself content-free. The pr ...
Judgment and consequence relations
... the variables from the constants. A constant is a proposition that does not change truth value. It is either true or false; if it is true, it is always true. If it is false, it must always be so. Variables can be either true or false, and — depending on circumstances — they are true here and false t ...
... the variables from the constants. A constant is a proposition that does not change truth value. It is either true or false; if it is true, it is always true. If it is false, it must always be so. Variables can be either true or false, and — depending on circumstances — they are true here and false t ...
EVERYONE KNOWS THAT SOMEONE KNOWS
... An example of a universally true formula in our language is ∀x (2x ∃y 2y φ → 2x φ), where variable y does not occur in formula φ. Informally, this statement means “if agent x knows that somebody knows φ, then agent x herself knows φ”. We show that this statement is derivable in our logical system in ...
... An example of a universally true formula in our language is ∀x (2x ∃y 2y φ → 2x φ), where variable y does not occur in formula φ. Informally, this statement means “if agent x knows that somebody knows φ, then agent x herself knows φ”. We show that this statement is derivable in our logical system in ...
