Levels of Infinity: Cantor, Hilbert's Hotel, and Tao's Non-Standard Analysis

An accessible tour of the hierarchy of infinities—from countable to uncountable—Cantor's diagonal argument and Hilbert's Hotel, to Terence Tao's non-standard analysis. We'll explore infinitesimals and infinite quantities treated algebraically via hyperreals and the transfer principle, and discuss the trade-offs of this approach. A math‑savvy journey blending classic proofs with modern perspectives.

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