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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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.
the notion of infinity though in calculus is really nothing more than what finite approximations are tending towards?
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But we get exact answers for Tangents and integrals in the majority of cases. This suggests that there is an exact method to obtaining these results that doesn't rely on approximations. Lagrange showed it for Tangents in his 1797 work "theory of analytic functions".
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That’s an interesting point
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