On Sun, Feb 9, 2020 at 12:29 AM Don Kelly <d...@shaw.ca> wrote: > _ _ _ HUH? 0 0 0 where i am using HUH? to indicate that for x=0 the > result is indeterminant. Creep up on 0 and no matter how close to 0 > you get -the results are the same. Crossing 0 is a discontinuous jump > directly from infinity to 0
indeterminant is a good way of putting this. On Sun, Feb 9, 2020 at 10:11 AM Henry Rich <henryhr...@gmail.com> wrote: > See https://arxiv.org/pdf/math/9205211.pdf esp. p. 6 I think you're referring to Knuth's allusions to Cauchy's treatment of Principal Value? I tried reading through Knuth's writeup there for his take on https://en.wikipedia.org/wiki/Principal_value in this context. But it felt like he only got close to that topic, without actually addressing it. Taking a few steps back, from my perspective (viewing mathematics as approaches for dealing with systems of carefully chosen constraints), An expression of the form: x = y ^ 0 can be viewed as a constraint on the value of x, such that y = y ^ 1 Or: x is a number which when multiplied by y gives a result of y. And, for example, if y is 2 then x is 1. But when y is 0, any number works for x. So, it's "indeterminant". This doesn't mean that 1 is an incorrect answer, but it does mean that it's not the only answer. But this particular situation is not the only example where mathematics allows for multiple answers. Square root is another example. In J, 1 = %: 1 even though 1 = _1 * _1 And functions like arcsin (_1&o.) have a theoretical infinite number of solutions, though it's common practice to neglect that issue when performing calculations. But the problem with 0^0 isn't so much that the result is unknown, but that it's difficult to even talk about a number which would not work in that context. And, that's dangerous ground for mathematical discussion. Anyways... in my opinion, this is definitely a "don't overthink it" topic. (What some people might carelessly call "a waste of time"). Thanks, -- Raul ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
