Building Mathematical Statements
Mathematical statements are exactly the same as fashion statements. Except instead of clothes, we have mathematical formulas. Hopefully we won't get chilly walking down the runway.
The simplest...
Conditional Statements
We make several kinds of statements every single day. Some of them are simple expressions of fact. You might say, "I'm going to Disneyland today!" or, "My favorite ride is Space Mountain!" or, "...
The Quality of Equality
Understanding equality, or sameness, is a universal theme in all areas of mathematics. When mathematicians say, "2 + 2 = 4," they mean that the two things on either side of the equal sign are liter...
Proofs
When detectives Benson and Stabler search a suspect's apartment, they aren't looking for just anything to give to the prosecutor. They need solid, tangible, and legally obtained evidence. (Although...
Proof by Deduction
Deduction is a type of reasoning that moves from the top down: it starts with a general theory, then relates it to a specific example. We start with a broad statement that we know to be true, and t...
Proof by Induction
Deduction is all about going from general theories to specific examples. Induction flips this whole shebang around, like a fun-house mirror. Inductive proofs go from the bottom up: we start with a...
Induction in Action
All this talk about mathematical induction might sound pretty abstract at first, so let's run through another specific example, yeah? Actually, let's walk through it, nice and slow-like.Sample Prob...
Proof by Contradiction
The proofs we've looked at so far have been all about directly proving something is true. That seems pretty obvious, but sometimes it's simpler to prove something isn't true. The truth is fun and a...