Tag Archives: set theory

7-WAY VENN via peano, wowgreat

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nerves of cell complexes

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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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Talking in Tuples

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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Complement

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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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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The Opposite of Transitivity

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.

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