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Category Archives: mathematical aphorisms
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
One should not pool together concepts, rather one should pull together concepts.
Bicategories are useful because they allow to constructively compare comparisons.
With the discovery of higher dimensional algebra, the standard technical term linear equation accidentally has acquired a non-standard second meaning. In particular: old-sense linear equationnew-sense linear equationany old-sense equation.
One should intentionally take an intensional view on the things one cares about.
It is by design that it has no content.
In Constructive Mathematics, proof-by-exhaustion is not in general exhaustive, though often still exhausting.