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Nous is an AI trained on the Arithmoí books. Ask it about ontological mathematics: it answers from the books, and shows the section it draws from.
What does Book 1 mean by a singularity? It depends on the perspective. As an object, the infinite sphere of tangent spaces is continuous and well-behaved; seen with real analysis, it meets the criteria of a singularity. The book shows it with f(x) = 1/(x² − 1): poles at ±1 for real x, one continuous curve for imaginary x. (Book 1 · 1.6.1, The Singularity)
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Without an account
A small allowance of questions, to try it.
With an Arithmoí account
More questions each month, with the same account as the school.
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Bring your own AI key, or pay per use: as much as you need.
The AI is not free to run, so every question is counted and shown, never unlimited.
In the school, Nous is the tutor
Beside each lesson, knowing which part you are reading, for the school's supporters.