logic

Wanna get good at fighting with your words?

I want the truth! Since logic is all about the study of true and false, we need some sort of basic type of object that will represent and store these true and false values.

Remember, you’re doing math Now that we have propositions which are the basic items of true and false, we will now define operators that we can use to create functions that take in one or more propositions, and output some truth value that represents the result of “combining” our propositions in different ways.

Why do we prove things? In mathematics everything needs to be rigorously proven in order for it to be truly accepted and believed as rule. This runs counter to a lot of other fields in which something is to be believed true if there is sufficient evidence supporting it.

Contradiction with Style Wait, How the Fuck did we get Here? Last section we showed that the most obvious way to prove things is to start with something that we know is true, and then take a bunch of true steps from there to get to our eventual claim that we were trying to show.

Simple Notation Before we get into the discussion of quantifiers, lets take a little breather to show some math notation and say what it means. The crazy thing is that mathematicians are lazy af and will take the opportunity to write things in shorthand.

Proofs Seem so Hard, How do I get Better at Writing Them? Before we get in to the practical application of logic and proofs to your (a CS student’s) career, we will first make a detour to answer a question that I often get when talking about proofs to students who are unfamiliar with them.

This page will use a small amount of information from the chapter on Set Theory. It is not required, but understanding sets might be helpful to get how induction works.