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Tag Archives: generalised numbers
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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Tagged arithmetic, bazooka, cardinal number, cardinality, cardinals, children, elementary school, generalised number, generalised numbers, Georg Cantor, gradeschool, infinite, infinity, kickball, kids, math, mathematics, maths, money, noncommutative, noncommutative operator theory, noncommutative operators, noncommutativity, numbers, objectoriented programming, ontology, operator overloading, ordinal number
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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
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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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 Infiniteness. I would imagine myself in a spaceship … Continue reading
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Tagged ∞, c, generalised number, generalised numbers, God, imagination, infinity, light speed, math, mathematics, maths, meditation, mind, number, physics, recursive, religion, special relativity, stereographic projection
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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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Tagged angle, corpus, cryptography, education, field, force, Fourier series, functional analysis, generalised number, generalised numbers, jpeg, linear algebra, linear transforms, long reads, math, mathematics, maths, number, Photoshop, science, shearing, signal analysis, Taylor series, thermodynamics, vectors
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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
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