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How big is the universe? It's so big that it's bigger than itself. (Russell's Paradox)
We investigate infinity with set theory, which deals with sets - collections of things, like the set of all natural numbers and the set of all polygons. Sets can contain anything (including sets) and can be however large. But even though a set can be easily larger than the entire physical (not just the observable) universe, there are sets that are too large to be a set. One of them is the set of everything (a.k.a. the universal set). Known as the Russell’s Paradox, the proof itself is as spectacular as the result: the attempt to create a foundation for math through set theory accidentally created a creature too large to be contained.
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Speaking Faster (by a million times) Changes the World
If we can speak faster (roughly a million times faster), we can tell people who have never tasted chocolate what chocolate tastes like, we won’t need education or specialization, and we’ll live in a much better world.
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Use Ad-blocking DNS to Block Ads everywhere
If you want to block ads everywhere for any device without installing any apps, including in TV boxes and mobile games, you can use a DNS server that blocks ad. Here I go over briefly how you can set it up and how it works.
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What is du?
When I first learned integrations by substitution, I saw \(\frac{\mathrm{d}u}{\mathrm{d}x}\) get rearranged to \(\mathrm{d}u=⋯\mathrm{d}x\). My first reaction when I saw it was
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The Prisoner's Climate Crisis
For the first time in history, Time magazine awarded the “Person of the Year” title not to someone who has made a significant impact in the past, but to someone who gives people hope for the future.