Mathematical Unity: A Journey Through Structures, Patterns, and Ideas
Exploring the deep connections across pure mathematics through a natural evolving pathway.
Numbers evolve: ℕ → ℤ → ℚ → ℝ → ℂ. Infinity reveals different “sizes” (countable vs uncountable). Foundation for set theory and analysis. Cantor’s diagonal argument = deep philosophical shift.
Exercises
- Prove √2 is irrational.
- Show ℚ is countable but ℝ is not.
Test Your Knowledge
Resources
reading
reading