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Mathematics in Society
After several conversations recently about the social status of mathematics, I thought I’d put here links to two short essays I wrote on this. 1. An exchange on Mathoverflow 2. Mathematical Vistas
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Linear independence of polynomials
One of the exercises this week asked for a proof of linear independence for the set inside the polynomials with real coefficients. However, note that the polynomials here are regarded as *functions*...
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A vector space of uncountable dimension
Let be the real vector space of all functions from the natural numbers to the reals. Then has uncountable dimension. To see this, for each , let be the function such that . Claim: The are linearly...
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