01. Foundations

Foundations

I started out with an axiom less proof because I want the reader to keep in mind that there are other ways to represent polynomials. Most higher mathematics textbooks and papers start off with definitions which don't provide insight on what they actually want to accomplish. This type of writing style is known as first order logic. Additionally, I kept the definition of y general because I wanted the reader to know that it could be anything, not just an integer or a real number. I realized that if I kept it in first order logic, which is in the language of predicate calculus seen in traditional mathematics, I would hit a point where I could not get past Godel's Theorem intuitively so that I could get past the construction. Hence, why I drew up this type of proof and I think it should make a lot more sense intuitively and logically to the reader.

Exercises

1. What is the opposite of each other?

2. What are some ideas that contradict one another?

3. What does a number mean to you?

4. What does a word mean to you?

5. What does a sentence mean to you?