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Category Archives: expository
Reading Bolzano. Part 1.
The next installment brings few surprises. Bolzano argues for dividing knowledge into parts, and for interlinking those parts, within reason. It is a little surprising (to me) that Bolzano that early in his text defines what he means by ‘Wissenschaft’, … Continue reading
Posted in expository, Olds, Philosophy
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Mathematical Aphorisms. Part 6.
It seems underemphasized that the parsimony of ZFC in the way of ‘types’ (having only one sort called sets) has the following practical and notational virtue: you can get by with a single type of the quantifier , and a … Continue reading
Posted in Category Theory, expository, logic, Olds, Research
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Reading Bolzano. Part 0.
This serial will provide, in many and short installments, created every now and then, provide a new translation into English of, and commentary on, the German original of Bernard Bolzano’s 1837 classic book ‘Wissenschaftslehre’. I omit the frontmatter and table … Continue reading
Posted in expository, logic, Olds, Philosophy
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Higher Trees Today. Part 0.
For the time being, the installments of the serial ‘Higher Trees Today’ will focus on three kinds of higher trees: Contractible Spaces of Choices (c.s.c.) Diestel–Oum decompositions (d.o.d.) Kalai trees (k.t.) MasbaumVaintrob trees (m.v.t.) Of course, while the latter three … Continue reading
Posted in expository, Higher trees, Mathematics, News, Olds, Research, Simplicial complexes, Structure theory
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Vignettes. Part 13.
There probably is no better illustration of the vagaries of notational fashion than the fact that nowadays, the numeral 1 is commonly used to denote the (conceptually very important) terminal category, while George Boole 170 years ago used 1 to denote … Continue reading
Posted in Category Theory, expository, Mathematics, Olds, Vignettes.
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Vignettes. Part 12.
Did you know that mathematics will provide you with moreorless standardized tools to usefully express commonlyoccurring ideas? For exaple, the following illustration contains at least three examples of this: (0) the symbol for boundaries of things, the symbol to symbolize … Continue reading
Posted in digraph theory, expository, Mathematics, Olds, Research, Technology.
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Mathematical Aphorisms. Part 5.
Perhaps the best example1 of a sound and complete proof system for a general audience are the three Reidemeister moves. 1 Calling Reidemeister moves a ‘proof system’ goes back at least to Avi Wigderson’s 2006 ICM contribution.
Posted in expository, mathematical aphorisms, Olds
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