Well this is ironic I mean, sure, no one can force you to accept this as true if you don't want to -- that's the whole point of this conversation! Everyone has their own idiosyncratic language about numbers they use on their head to understand the world and that's fine!
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Replying to @arthur_affect @JustCanadian7 and
But from the point of view of standard, accepted, classroom mathematics you're just wrong 0.9999... = 1 is, according to the normal rules, true You can get into an extremely formal proof of it via real analysis, but you can demonstrate it informally with simple algebra
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Replying to @arthur_affect @JustCanadian7 and
Ever since this debate became an Internet meme there's been mathematicians pointing out that *you don't have to* accept this if you don't want to You don't have to do anything, in math, math is a construct you choose to adopt for your own purposes
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Replying to @arthur_affect @JustCanadian7 and
Your whole "equivalent to but not equal" thing, for instance, is a matter of much discussion - the = sign does indeed mean different things to different people at different times It's valid, you can say that if you want
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Replying to @arthur_affect @JustCanadian7 and
There are *consequences* though Phrased differently, saying 0.999999... cannot equal 1 is saying you reject the concept of a limit (it's really saying that there is no such specifically constructible number as 0.9999..., you refuse to allow the 9s to go on into "infinity")
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Replying to @arthur_affect @JustCanadian7 and
And the concept of a limit is what calculus depends on If you reject it, then you just reject calculus Which, again, is fine! You don't need to accept calculus if you don't want to! I only took AP Calculus because of pressure from my parents and my crush on the teacher!
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Replying to @arthur_affect @JustCanadian7 and
In fact there's plenty of specific evidence from physics now that calculus does not reflect "underlying fundamental physical reality" (whatever that might mean) The real world isn't actually continuous, it's discrete, it has pixels
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Replying to @arthur_affect @JustCanadian7 and
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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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
And don't use any Zebra Crossings, especially after putting a fish in your ear.
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End of conversation
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