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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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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 BanachTarski 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 graduatelevel mathematics course. These peculiarities … Continue reading
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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Tagged ℝ, ∞, education, generalised number, generalised numbers, Georg Cantor, Giuseppe Peano, imagination, infinity, iuseppe Peano, math, mathematics, maths, mental space, number, projective geometry, real numbers, science
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Is Calculus Bull*hit?
The hallmark of a calculus course is epsilondelta proofs. As one moves closer and closer to a point of interest (reducing δ, the distance from the pointofinterest), the phenomenon’s measure is bounded by something times ε, a linear error term. … Continue reading