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He strongly objects to the use of infinity and proofs and mathematics that involve it, which includes real numbers He is not alone, this is a known branch of m
by szemet 9y ago
He strongly objects to the use of infinity and proofs and mathematics that involve it, which includes real numbers
He is not alone, this is a known branch of mathematics called finitism: https://en.wikipedia.org/wiki/Finitism https://en.wikipedia.org/wiki/Finitism
- agumonkey 9y agoThanks for this link !
- danieltillett 9y agoThe problem is not so much infinities in mathematics (after all mathematics is just a game with any rules you care to create), but if mathematics with infinities should be used when modelling the real world. I am certainly happy to be corrected, but I don’t think we have found any event in nature that requires infinities to explain it.
- rlpb 9y agoGeometry? Pi is an infinite series, as are the trigonometric functions. How can you explain the circumference of a circle without invoking pi?
- srean 9y agoAs long as \epsilon != 0 one can make rational_of(\Pi, \epsilon) an arbitrarily close approximation of \Pi, without the need for infinity. In fact that is precisely what we use in practice, by that I mean computation. Ultimately it comes down to a trade off. Which axiomatic system does one to work in ? Introducing infinity does have its fair share of warts (by warts I mean consequences that flies in the face of intuition).
- rlpb 9y agoHow do you approximate pi in this way without making use of an infinite series? Or are you saying that an approximation that doesn't use an infinity is fine even if an infinity was used to arrive at it?
- srean 9y agoIts the latter. You can truncate the series at an appropriate place of your choosing. But yes, \Pi as a number does not even exist unless you add the Reals, so that would need infinity. What I am saying is, one can work with the Rationals.
- widdma 9y agoPi isn't an infinite series, it is just a number. Sure, it can be represented as an infinite series, but so can any number! (Eg. 1 = 0.999999...)
- tinus_hn 9y agoThe difference obviously is that you can't represent pi as a finite series or a repeating infinite series while you can do that with the rational numbers.
- vinchuco 9y agoThough mathematics does not wait for justification, here's something to think about: infinite decimals https://en.wikipedia.org/wiki/Square_root_of_2 https://en.wikipedia.org/wiki/Square_root_of_2
- widdma 9y agoEvery number has an infinite decimal expansion. 1 = 0.999... 1/2 = 0.49999... etc. In some ways it's a property of the representation, not something intrinsic to the number.
- deleted 9y ago[deleted]
- a_t48 9y agoIsn't the time needed for an object to accelerate to the speed of light infinite?
- danieltillett 9y agoYes, but this is just a different way of saying it is impossible.