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Tag Archives: the continuum
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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Tagged axiom of choice, ℝ, ∞, big, continuum, Dedekind cut, functionals, G. H. Meisters, Henri Lebesgue, infinite, infinity, math, mathematics, maths, measure, measure theory, real numbers, Richard Dedekind, set function, set theory, size, the continuum
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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
Human Mathematics 