Deriving a Quine in a Lisp

As with my previous post, this post is another excerpt that will be included in my final Master’s thesis, but I decided it is interesting enough to post it on its own.

We start with a definition of diagonalization (or quotation), as discussed in The Gödelian Puzzle Book:

Definition 1: For an expression P in which a variable x occurs, we say that its diagonalization D(P(x)) is the substitution of the variable x with the quoted expression P(x).

This definition allows us to represent self-referential expressions.

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Equational reasoning in Racket

This post is an excerpt that will be included in my final Master’s thesis, but I decided it is interesting enough to post it on its own.

We will define a few of Peano’s axioms together with a procedure for substitution in equations so that we can prove some theorems using this system.

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Stay Home

I would like to mathematically demonstrate how important it is to stay home in times like these. My article will be a very short version of the cite below. Let’s start with a simple task:

Begin by asking how a rumor might spread among a population. Suppose on Day 1 a single person tells someone else a rumor, and suppose that on every subsequent day, each person who knows the rumor tells exactly one other person the rumor. Have students ponder, discuss and answer questions like: “How many days until 50 people have heard the rumor? 100 people? The whole school? The whole country?Exponential Outbreaks: The Mathematics of Epidemics

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