On Tuesday, October 30, 2018 at 4:55:13 AM UTC-5, Bruno Marchal wrote: > > > On 29 Oct 2018, at 23:48, Philip Thrift <[email protected] <javascript:>> > wrote: > > > > On Monday, October 29, 2018 at 5:15:28 PM UTC-5, John Clark wrote: >> >> >> On Mon, Oct 29, 2018 at 5:21 PM <[email protected]> wrote: >> >> >*If you try to traverse a unit distance in infinite steps such as 1/2, >>> 1/4, 1/8, 1/16 and so forth, the sum converges to 1, but you will never >>> traverse the distance even though the sum converges.* >> >> >> Never? If what you say is true then calculus is wrong. I don't think >> calculus is wrong. >> >> John K Clark >> >> >> >> > > > To a mathematical *ultrafinitist* [ > https://en.wikipedia.org/wiki/Ultrafinitism ], the standard calculus is > wrong. > > One can salvage some version of standard calculus, but a lot of care is > needed to never define any process that assumes a completed infinite number > of steps. > > > That is finitism. Ultrafinitisme asks for a bigger natural numbers. It is > close to nonsense for me, but finitism accept the potential infinite and > reject actual infinite. Ultra-finitism rejets both potential and actual > infinite. > > With mechanism, the ontology is finitists (not ultra-finitist), and the > many phenomenologies is unbodundably big, beyond the infinite, somehow. > > Bruno > > > > In any case, doing all of math on computers *here on Earth* makes one explicitly an ultrafinitist because there are only a limited, finite number of bits one can ever have available!
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