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When there’s a confusing problem and you’re just starting out and you have a falsifiable hypothesis, go test it. Find some simple, easy way of doing a basic check and do it right away. Don’t worry about designing an elaborate course of experiments that would make a grant proposal look impressive to a funding agency.

Harry Potter and the Methods of Rationality

Eliezer Yudkowsky

in order to be able to draw a limit to thought, we should have to find both sides of the limit thinkable (i.e. we should have to be able to think what cannot be thought)

[Routledge Classics] Ludwig Wittgenstein - Tractatus Logico-Philosophicus

2001, Routledge - libgen.lc

The main difference between integrability in the sense of Lebesgue and Riemann is the way we measure 'the area under the curve'. The Riemann integral asks the question what's the 'height' of 𝑓f above a given part of the domain of the function. The Lebesgue integral on the other hand asks, for a given part of the range of 𝑓f, what's the measure of the 𝑥x's which contribute to this 'height'.

Integration - ELI5: Riemann-Integrable vs Lebesgue-Integrable - Mathematics Stack Exchange

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