*This gallery contains 6 photos.*

nerves of cell complexes

7-WAY VENN via peano, wowgreat

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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Mathematics is the *Most* Different Language. In Can we make mathematics intelligible?, R P Boas jokes: There is a test for identifying some of the future professional mathematicians at an early age. These are the students who instantly comprehend a sentence … Continue reading

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Tagged Chinese, clarity, comprehension, definitions, English, function, functions, group theory, intelligibility, inverse mapping, inversion, language, Mandarin, math, mathematics, maths, measures, metrics, operation, operator, order theory, ordering, partially ordered set, poset, Ralph Philip Boas Jr., reading, relation, set, set theory, Tagalog
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Here’s an inside-out thought: The air around us is a 3-manifold with 3-holes where solid objects are, and the 2-boundary is the ground. Or if you think of all the sky, it’s a spherical 3-shell (with one 3-hole, the Earth) floating … Continue reading

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Tagged boundary, childlike thinking, children, complement, inside-out, kids, logic, manifolds, math, mathematics, maths, set theory
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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

rock ≻ scissors ≻ paper ≻ rock “beats” is not a transitive relation. in fact, Rochambot is an example of Logical Circular Logic. Rochambot obeys the non-wellfoundedness axiom (it’s a stream). it’s the cyclic group P₃.