I think the main thing that mathematical finitists get wrong is that numbers “actually” exist—let alone ought to be a certain way.
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As a finitist, I just prefer my theories stay within the realm of things hat can be explicitly exhibited. It's helpful that I can do lots of calculus in the context of this perspective tho, otherwise I wouldn't be wasting my time.
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Processes that can be completed before the universe ends. Like computing triangle ratios. Why would I settle for an approximate answer that gets better the more work I do when I can get an exact answer in a predicatably finite number of steps?(angles vs spreads in rational trig)
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But why are you subjecting mathematics to constraints of what’s physical?
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Finitist that doesn't provide new pathways to old problems is a waste of time, but actually lots of beautiful math is possible without reals or limits. Obvs twitter is not the place to provide through evidence to this claim, but I intend to do it in the right medium.
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the notion of infinity though in calculus is really nothing more than what finite approximations are tending towards?
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