Tag Archives: generalised number

What Comes After Infinity?

When I was in kindergarten, we would argue about whose dad made the most money. I can’t fathom the reason. I guess it’s like arguing about who’s taller? Or who’s older? Or who has a later bedtime. I don’t know … Continue reading

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Paul Finsler believed that sets could be viewed as generalised numbers. Generalised numbers, like numbers, have finitely many predecessors. Numbers having the same predecessors are identical. We can obtain a directed graph for each generalised number by taking the generalised … 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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Vectors

Vectors, concretely, are arrows, with a head and a tail. If two arrows share a tail, then you can measure the angle between them. The length of the arrow represents the magnitude of the vector. The modern abstract view is … Continue reading

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Pythagorean Theorem This is how I first really understood the Pythagorean Theorem. The outer circle looks just a little bit larger than the inner circle. But actually, its area is twice as large. Kind of like the difference between medium … 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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