left_adjoint
/
class-notes
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

more

This commit is contained in:
clarissa 2023-09-06 20:38:53 -07:00
parent a88f4d68a6
commit 73ea46cd9d
1 changed files with 19 additions and 1 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

20
cs250/classnotes.org
View File

@ -52,7 +52,25 @@ For now, I'll say a proof is a way to convince the reader, by clearly outlining
And in the next section we'll cover a bit more about what that definition means.
** What is logic, what is a proof?
So in the last section we established that
So in the last section we established that the point of the course is to develop the logical and mathematical tools that will let us study programs, their behavior, and their properties in an /abstract/ way independent of programming language or hardware.
Now we want to introduce some of the basic mathematical concepts and formaliss we need to start down this path.
The very first thing I want to discuss is /what logic is/.
So logic is, and I'm borrowing from Dr. Logic's excellent lecture series (insert link) for this definition, a way to determine truth of statements from their premises by the employment of /arguments/ that are a series of valid reasoning steps.
In the context of mathematics, we call a valid argument a proof.
Proofs are the bread and butter of what mathematicians /do/. They're how we convince ourselves and each other that those moments of insight and creativity we have are actually true and not just wishful thinking.
Here's an example of a very simple insight and proof.
Let's say you were thinking about the /natural numbers/. That is the numbers that are either zero or a positive whole number. You realize "hey, thare are a lot of these. There's gotta be an infinite number of them." and now you want to convince yourself this is /true/, in other words you want to /prove/ it.
To start, you have a rather clever guess on how to show this. First, you note that if you have a natural number you can always add one and it stays a whole, positive, number. Second, you decide to see what happens if there's a *finite* amount of natural numbers. You're going to /assume/ that this is true and then see if you can show it leads to something weird.
** Variables and formulae
* Module 2
* Module 3