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It is well-known that bijection between $\textbf{R}^p$ and $\textbf{R}$ exist (e.g. here, though many other examples exist). The problem with all these examples of bijections is that typically the ...

in a recent MO question, link, discussing the current foundations of mathematics, the author linked a video lecture by Prof. Voevodsky, which argues against the principle of $\epsilon_{0}$-induction ...