Writing
3 posts tagged "Set Theory"
We explore the Axiom of Choice, its equivalence with Zorn's Lemma and the Well-Ordering Principle, the controversies surrounding it, and its indispensable role throughout modern mathematics.
We explain the Banach-Tarski paradox — how a solid ball in three-dimensional space can be decomposed into finitely many pieces and reassembled into two balls identical to the original — and explore the role of the Axiom of Choice.
We present Cantor's diagonal argument proving that the real numbers are uncountable, explore its consequences for set theory, and examine how it forever changed our understanding of infinity.