Therefore calculus, which started out based on the assumption of a continuous world (the "infinitesimal"), is a shortcut, a kludge It lets you calculate shit faster than counting up all the particles or whatever that are actually there
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Replying to @arthur_affect @JustCanadian7 and
And again, that's fine All of math is that Adding up integers is that (Zeno's paradoxes were his attempt at demonstrating all numbers higher than 1 are a lie, and honestly they remain pretty convincing)
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Replying to @arthur_affect @JustCanadian7 and
But infinite Sums show resolve Zeno's paradox and show he was wrong basically.
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Replying to @wrarebit @JustCanadian7 and
They only do that if you believe in the idea of limits and infinite series and don't think they're stupid Zeno did think so Our JustCanadian7 friend also thinks so, and they are entirely entitled to that belief
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Replying to @arthur_affect @wrarebit and
If my Canadian colleague finds themselves accidentally stumbling into a convincing argument that the integers themselves aren't real after arguing that limits aren't real, well, you take risks when you start messing around with philosophical realism Wear a helmet
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Replying to @arthur_affect @wrarebit and
We an argue about whether infinites and infintesimals exist, but we are very confident that they are not real, in the sense that they are not real numbers, a defined set that excludes them. Whether the real numbers are real is up to you.
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Replying to @mssilverstein @wrarebit and
I mean, infinites and infinitesimals are highly problematic to work with, which is why calculus itself was highly problematic for a long time -- people *hated* that you need to talk about "infinitesimals" to talk about calculus And yet calculus is really fucking useful
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Replying to @arthur_affect @mssilverstein and
It was a great big dilemma and multiple people (Newton, Cauchy, etc) worked really hard over a century to try to find a way to say what calculus was about without using words like "infinite", to "banish the infinitesimal" It's fun to read about
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Replying to @arthur_affect @mssilverstein and
I mean it's this kind of thing that makes the human process of doing math fun to learn about and that demystifies this idea that mathematical truths are holy tablets received from God
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Replying to @arthur_affect @mssilverstein and
My hot AP Calc teacher when teaching us the delta-epsilon definition of a limit said "You don't actually need to know this to do calculus but mathematicians fought over it for a hundred years so the least you can do is know what it is"
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(One of the many reasons I was smitten A shining light among small town high school mathematics faculty)
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