A tree is a connected graph with no cycles. One of its vertices is designated to be the root. If not, then it's a free tree instead of a rooted tree. A group of trees is a forest.

If you add an edge to a tree, a cycle is created. If you remove an edge from a tree, it's disconnected.

• ... that any two consecutive integers have opposite parity?
• ... that \(0\) is not positive or negative, but instead non-positive and non-negative?
• ... that to disprove an existential statement, you need to prove a universal statement?
• ... that any compound proposition can be rewritten as a disjunction of conjunctions?
• ... that the act of using a truth table to determine the logical equivalence of two compound propositions has an exponential time complexity?
• ... that implication is a transitive relation on the set of propositions?
• ... that knowing the prime factorizations of two integers allows for their greatest common divisor and least common multiple to be efficiently computed?
• ... that after over \(1000\) years, the Euclidean algorithm is still in use?
• ... that the principle of mathematical induction, the principle of strong mathematical induction, and the well-ordering principle are all logically equivalent to each other?
• ... that there exists a pair of Londoners who have the exact same number of hairs on their heads?

May 12, 2024

Discretopia is complete! After over 500 days, the project has come to an end.

It's been a long journey, and I've learned so much along the way, both about discrete math and making websites. To have made it this far means a lot to me.

Readers, I hope this website helps you learn something, or simply makes you smile :)

March 13, 2024

With 133 entries, Discretopia is now officially content-complete. All the topics I set out to cover back in December 2022 can be found in the journal.

In the last stage of development, I'll add a few more features, review every entry one last time, improve the mobile experience, and then finalize the website's overall design.

This is a major milestone! My vision for this website will soon be fully realized. For now, enjoy the most comprehensive version of Discretopia yet!