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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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Do numbers exist?

When I was a math teacher some curious students (Fez and Andrew) asked, “Does i, √−1, exist? Does infinity ∞ exist?” I told this story. You explain to me what 4 is by pointing to four rocks on the ground, … 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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Religious Infinity

When I was young, I used to — as an exercise — try to conceive of ∞. We would hear in Sunday School that God is Infinite, that you can’t comprehend God’s Infinite-ness. I would imagine myself in a spaceship … Continue reading

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