Tag Archives: real numbers

Measure: Sizing up the Continuum

For those not in the know, here’s what mathematicians mean by the word “measurable”: The problem of measure is to assign a size ≥ 0 to a subset of ℝ. In other words, to answer the question: How big is that? Like, how big … Continue reading

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Nonterminating decimals do not make sense.

The Banach-Tarski paradox proves how f#cked up the real numbers are. Logical peculiarities confuse our intuitions about “length”, “density”, “volume”, etc. within the continuum (ℝ) of nonterminating decimals. Which is why Measure Theory is a graduate-level mathematics course. These peculiarities … Continue reading

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Math Infinity

Conceiving of ∞ as a mathematician is simple. You start counting, and don’t stop. That’s all. ($i++ for programmers) Which is why ∞ seems very small to the mind of a mathematician. With projective geometry you can map ℝ to … Continue reading

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Is Calculus Bull*hit?

The hallmark of a calculus course is epsilon-delta proofs. As one moves closer and closer to a point of interest (reducing δ, the distance from the point-of-interest), the phenomenon’s measure is bounded by something times ε, a linear error term. … Continue reading

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