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  • fossilesque

  • R wins again! I'm grateful every time i write the vector 1:n

  • Before trump 2 electric boogaloo this was one of my biggest dreams..

  • Semantic round brackets make typst impossible to use for me. If it had curlies instead it would be great.

  • This is just not true. The normal limit we have here means a limit would have to exist from both directions and they should be equal. They're not, so the limit doesn't exist.

    One-sided limits would be denoted by x -> 5– and x -> 5+ or similar.

    PS: in complex analysis, there is no distinction between +infty and -infty, so there it would be correct to say the function has limit infty at 5.

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  • They work with the Gates Foundation, which pressured Oxford University into selling exclusive rights to their covid vaccine to Astrazeneca, after promising it would be free to all manufacturers.

    Educational channels especially should choose their sponsors wisely.

  • So basically R markdown?

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  • Depending on the context (was the whole paper built on wrong assumptions or was there just some small error) that can still be a good thing?

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  • Yes

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  • Extinct!

  • Sometimes when I'm really tired in the morning I get out of bed like this, it's the path of leadt resistance.

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  • A practical application is for example in probability theory (or anywhere that deals with measures) such as this question:

    If we generate a random real number from 0 to 1, what is the probability that it is rational?

    Because we know that the continuum is so much larger in a sense than the set of rationals, we can answer this confidently and say the probability is zero, even though it is theoretically possible for us to get a rational number.

    Statistics deals with similar scenarios quite frequently, and without it we wouldn't have the modern scientific method.

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  • There are infinitely many rational numbers between any two integers (or any two rationals), yet the rationals are still countable, so this reasoning doesn't hold.

    The only simple intuition for the uncountability of the reals I know of is Cantor's diagonal argument.

  • I think for straight 4/4 (so not felt in half time) 140 and above is definitely fast, considering the vast majority of music falls in the 110-130BPM range.

  • Basically an exponential function.

  • It is just a definition, but it's the only definition of the complex exponential function which is well behaved and is equal to the real variable function on the real line.

    Also, every identity about analytical functions on the real line also holds for the respective complex function (excluding things that require ordering). They should have probably explained it.

  • Linnutee in Estonian, literally "bird's path" because of the birds migrating south for the winter using it for navigation.