Categories » Logic

 Posts Logic: QuantifiersSome sentences feel an awful lot like statements but aren't. For example, $n$ is even This is not a statement because it doesn't have a truth value; unless we know what $n$ is, we can't really do much. Definition. A sente (More) Logic: Conditionals  So far our statements haven't been very interesting. In fact most mathematical statements of interest are things like If a function is differentiable, then it is continuous. These statements are known as conditional, because they depend o (More) Logic: OrLet's get another little word. Definition. Given two propositions $P$ and $Q$, the proposition $P\vee Q$ (read $P$ or $Q$) has truth value as given below: $P$ [l (More) Logic: Not & AndStatements by themselves aren't that interesting; let's see how to combine them. "not" A writing teacher once told me the best way to clean up your writing is to eliminate as many adverbs and adjectives as possible. But one very important adverb--w (More) Logic: OverviewQuando orientur controversiae, non magis disputatione opus erit inter duos philosophos, quam inter duos Computistas. Sufficiet enim calamos in manus sumere sedereque ad abacos, et sibi mutuo dicere: Calculemus! When controversies arise, there will (More) Logic in Proofs[callout headingicon="noicon" textalign="textright" url="https://www.youtube.com/watch?v=OncDlwNH9F0" target="true" type="basic"] If man is five, then the devil is six. And if the devil is six, then god is seven. This monkey's gone to heaven. Black F (More) Logic: UniquenessThere is another quantifier, besides existential and universal: the unique existential quantifier. Definition. The sentence \$\exists!x:S(x)\$ is true if there is exactly one \$x\$ in the universe so that \$S(x)\$ is true. We read There is a unique \$x\$ suc (More) Logic: Proofs with QuantifiersNow we're at the stage where you're probably antsy to start actually writing proofs. Excellent! Let's get started. [pullquote color="reynoldsred" align="alignright"]The logical form of a statement indicates the structure of its proof.[/pullquote] T (More)