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")
1 reply 2 retweets 20 likes -
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
1 reply 3 retweets 12 likes -
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 just don't go off on this shit about things being fundamentally objectively true or false or real or fake With numbers, especially, that's just silly I mean you're now the "2+2=5" guy, do you understand that "Limits doesn't real, calculus is a fake"
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Replying to @arthur_affect @JustCanadian7 and
Have we done "the sum of all the positive integers is negative one twelfth" yet? I always liked that one as a "wait, what" maths moment....
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Replying to @social_scifi @arthur_affect and
It's great because it is both not at all what addition means and it's actually incredibly useful anyway.
1 reply 0 retweets 1 like
It was proven* to be true* in physics, by experiment, even
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