To an ultrafinitist, there is no such thing as a number that is inexpressible.

Right, but to be clear, it's not that ultrafinitists like Wildberger believe that they can express all the real numbers; rather, they believe that those inexpressible real numbers don't actually exist.

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vlovich123 4 days ago | parent [-]

How does that work for calculus which regularly looks at the limits of functions as x approaches infinity and has very real real world applications that stem from such algorithms?

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LPisGood 3 days ago | parent | next [-]

Here is a paper on just how a serious ultrafinitist copes with that https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/...

The short answer is that they deal with such things symbolically.

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drdec 4 days ago | parent | prev [-]

Math in general needs to have a big blinking "don't confuse the map for the territory" label on it.

E.g. when you calculate the area of a plot of land do you take into account the curvature of the Earth? You have to make a bunch of compromises in the first place to even talk about what the area of a plot land means.

Math is a bunch of useful systems that we humans have devised. We tend to gravitate towards the ones that help us describe and predict things in the real world.

But there is plenty of math which doesn't do either. It's just as real as the math that does.

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vlovich123 3 days ago | parent [-]

I agree. I’m just trying to speak to the “realist” argument that Wilderberg presents claiming that some numbers aren’t real and there’s no point talking about them when they come from very practical mathematics let alone the ones that aren’t. In no way was I trying to claim that some part of maths aren’t real - I was trying to understand the consistency of what to me seems like a confusing argument to make.

	▲	kragen 3 days ago \| parent [-]
		I don't think uncomputable numbers "come from very practical mathematics"! Rather, they come from Gödel, Church, and Turing demolishing Hilbert's program of solving the Entscheidungsproblem once and for all. Possibly, if Hilbert had succeeded, that would have made it "very practical mathematics", or possibly not, but that counterfactual is reasoning from a logical contradiction. https://plato.stanford.edu/entries/church-turing/decision-pr...