An evergrowing list of theorems, proofs, and references. Algebraic and natural deduction proofs have been formalized in Isabelle. Proofs by method of truth table have been generated by computer program to ensure their validity. Whenever possible, I reference free resources, such as Khan Academy, Sarada Herke, Numberphile, ProofWiki, Wikipedia, etc. Failing that, I reference established mathematical texts.

Teachers of mathematics, high-school seniors, undergraduates, and amateur mathematicians. The index may also serve anyone learning Isabelle. It may also serve the working mathematician.

There are resources for learning proofs, and there are encyclopedias of mathematics. Sites like Wolfram MathWorld are great for theorems, but lack proofs. Projects like Metamath are great at organizing theorems and proofs, but are not pedagogical. This site is a middle ground. It will give you a direction, then prove everything you need to know. All will be built from first principles. My primary goal is to show the connections between the various number classes (naturals, integers, etc.) My secondary goal is to provide proofs that are easy enough that they can be introduced during a student's formal education. To answer questions such as "Why is real addition commutative?"

The cost is $3 per month or $30 per year. There will never be ads or a donation drive on the free or paid version of the index. Sample pages are available below, to give you an idea of what you're money gets you. This Website is a preview of the index. You can securely purchase the index, with proofs and references included, from Gumroad.

If you don't know how to prove theorems, but would very much like to learn, here are a couple free textbooks to get you started:

- Sphinx
- Syllogism
- Natural number addition
- Natural number minimum
- Natural number GCD
- Boolean algebra
- Rational number addition

## A

## C

- Cancellative
- Cantor's theorem
- Cartesian product
- Cartesian product of two graphs
- Central vertex
- Classical propositional logic
- Closed curve
- Cofunction identities
- Combinator calculus
- Commutative
- Completely multiplicative
- Complex addition
- Complex conjugate
- Complex multiplication
- Complex number
- Composition
- Composition of monotone functions
- Conjunction
- Conjunction and disjunction
- Constant rule
- Convex polyhedron
- Coprime
- Countable set
- Cross product
- Cycle graph
- Cyclic quadrilateral

## B

## E

## D

## G

## F

## I

- Idempotent element
- Identity element
- Identity mapping
- Identity rule
- Imaginary unit
- Implicational propositional calculus
- Infimum
- Infinite series
- Injection
- Integer
- Integer GCD
- Integer LCM
- Integer equal to
- Integer less than
- Integer less than or equal to
- Integer subtraction
- Integer triangle
- Integral drawing
- Intersection
- Inverse relation
- Involution
- Irrational number
- Isomorphism

## H

## J

## M

## L

## O

## N

## Q

## P

## S

## R

## U

## T

## V