1/0 = 0

Post by jibal » Sat, Aug 11, 2018, 8:41 AM UTC

ummonk wrote: post #436

anoplus wrote: post #420

Earlier quoted context omitted.

I like your point here. I think 1/0 = Infinity+ is a satisfying expression. Its a clear concept which can be visualized in a simple graph. I think 0/0 is a different concept than 1/0. It's a different expression. 0/0 doesn't explicitly express a particular "path" on the graph. We can call it (0/0) different names if we want. They can say 0/0 = "undefined". I am currently satisfied with 0/0 simply equals to 0/0, or si…

>I like your point here. I think 1/0 = Infinity+ is a satisfying expression. Its a clear concept which can be visualized in a simple graph. Except it isn't. It still depends on which side you take the path from - from the positive denominator or the negative denominator side. (This is why IEEE 754 has a single signless infinity).

Post by mdpopescu » Sat, Aug 11, 2018, 9:03 AM UTC

sclv wrote: post #340

a_wild_dandan wrote: post #330

Earlier quoted context omitted.

Look at it this way... Standard definition of division function, d: d(x, y) = x * y⁻, for all x and y EXCEPT 0 Author's modified, piecewise ( https://en.wikipedia.org/wiki/Piecewise ) definition: d(x, y) = x * y⁻, for all x and y EXCEPT 0 d(x, y) = 0, for y = 0 He's just adding 0 to the domain of d(x, y) to extend the definition, and deliberately not using xy⁻ for that particular element of the domain. No inverse nee…

I know what he's doing. The problem is when you make it a different function (even by just extending it) then you change its equational properties. So equational properties that held over the whole domain of the function no longer hold over the extended domain. This is repaired by modifying the equational properties. But the modified equational properties mean that you now have a different system than before. So the…

Post by nicops » Sat, Aug 11, 2018, 9:42 AM UTC

mlthoughts2018 wrote: post #224

drb91 wrote: post #206

Earlier quoted context omitted.

> It’s similar to computing NaN-mean or NaN-sum for an array of all NaN values (which returns 0). Why would you want to do this rather than validating understanding of the data before computing on this? > For purposes of updating the accumulator, the mean of an empty array is perfectly well-defined: it should add nothing to the acculator (add 0). That's not a mean, though, that's a quirk of how you decide to (incorre…

From your response I can tell you don’t do much numerical linear algebra work. Consider needs to vectorize a large column-wise mean calculation across columns of a large data matrix (where NaN values are sparse but appreciable). The NaNs might be perfectly reasonable, expected pieces of data, but you still want to understand the distribution of the non-NaN data, and adding extra work to filter it out first might be h…

Post by Veedrac » Sat, Aug 11, 2018, 9:47 AM UTC

binarycoffee wrote: post #452

semi-extrinsic wrote: post #437

Earlier quoted context omitted.

An example well-defined use case is if you want to compute a harmonic mean, e.g. x = 2/(1/a +1/b) This is a form of average where you are giving increased importance to the smaller number. It frequently pops up in science/engineering, e.g. in hydrology when you are computing flow of water underground. In this case, it's "obvious" that when e.g. a is zero, you want 1/a to be zero so you simply return b. There's typica…

Quite the opposite I would say: the harmonic mean can be seen as a very good justification for `1/0=inf` as the pragmatic choice. If, say, `a` is mathematically very small (and `x` is accordingly expected very small`) but `a` become zero due to rounding behavior, then having `1/a=inf` results in `x=0` which is arguably closer to the expected result than e.g. `x=2b`. As someone involved with numerical methods, I have…

Post by blablabla123 » Sat, Aug 11, 2018, 9:56 AM UTC

lucian1900 wrote: post #478

blablabla123 wrote: post #476

I must admit I prefer 1/0 not to be 0 in the "Common Algebra". But that might be because I come more from an Natural Science/Engineering background where continuity is something that is expected virtually everywhere. Not even Theoretical Physics text books mention that continuity of functions is required as it is so ubiquitous. 1/0000000.1=10000000, 1/0.00000001=100000000.0, ..., 1/0=0 would break that. In fact we ha…

JavaScript’s behaviour is just how floats work. They are the same in all languages. There is storage reserved as part of their representation to encode infinity and NaN. The issue here is hardware integers, which have no signalling bits beyond possibly sign.