When setting out to add a new axiom to a heavily studied area of mathematics, perhaps one should at least formulate an argument that isn't shown to be incomplete with the most basic wikipedia search.
1/0 = 0
41–50 of 593 posts
Re: 1/0 = 0
#42I.e. a short-circuit means current = 0 because it trips a fuse?
Re: 1/0 = 0
#43Oh, so 0*0=1 ?
If a hn title said 1*0=0 could you reply "Oh, so 1=0/0?" The entire point of the article was suggesting you can define a consistent system without multiplication and division being entirely symmetrical (as they already are not)
> without multiplication and division being entirely symmetrical (as they already are not)
What do you mean?
Re: 1/0 = 0
#44It is the average of 1/0+ and 1/0- So at least that's something
> So at least that's something
It's also nothing. :-)
Re: 1/0 = 0
#45I'm not seeing how the tweet is mocking the Pony developers. It seems to mirror the tone and the content of of the documentation in the screenshot. It looks like an absurdist spin on the ivory tower vs industry meme, and it doesn't make anyone the butt of the joke.
Re: 1/0 = 0
#46Earlier quoted context omitted.
I think OP means that nothing breaks mathematically. It is not inconsistent and not false, so you can work with it. The only issue is to deal specially with the case of division by zero, which you have to do anyways. Code that assumes that (x/y) * y = x is wrong if you don't check for y = 0, independently of what you define x/0 to be.
It is inconsistent. If 1/0 = 0, then 1 = 0*0.
Wait, if 1 / 0 = infinity, then infinity * 0 = 1
This seems just as bizarre, since zero times anything shouldn't become 1, no matter how big or how many times you do it.
Re: 1/0 = 0
#47Earlier quoted context omitted.
> You know.. dividing is like breaking something up.. If you divide by 2, you break it up into 2 pieces.. if you divide by 0, from some standpoints, you do have nothing, because you broke it up into 0 pieces, and 0 pieces is 0. And dividing by 0.5 is breaking into how many pieces exactly?
I guess its more flipped. How many pieces equal the whole, not how many pieces can the whole be broken up into. That's why you can't divide by 0, any number of nothing can't make a whole. So all that to say: We can't treat 0 like a number. *disclaimer: I have no math background whatsoever, this is just a fun topic.
And as it follows, if you divide by 0.00000000001, you can fit a whole lot of pieces in your original value... so what should dividing by 0 (which is even smaller than 0.000000001) naturally do? 0, or +infinity?
Re: 1/0 = 0
#48Earlier quoted context omitted.
> the many pieces of code that assume that (x / y) * y equals x The same issue if division by zero throws an exception. This is simply a more practical approach that dispenses with the exception handling (ie becomes a less irregular test case). Edit: Not buggy behavior, when expected.
I would say an exception is much more convenient. Buggy code that silently continues to run is very hard to debug!
I used to think the same way: let's throw an exception on divide by zero, and forget NaN like a bad dream! But then someone explained to me that it's common to feed a billion numbers into a long calculation, then look at the results in the morning and find them okay, apart from a few NaNs. If each NaN led to an exception, you'd come back in the morning and find that your program has stopped halfway through. So there's a certain pragmatism to having numeric code silently continue by default.
Re: 1/0 = 0
#49Earlier quoted context omitted.
It is inconsistent. If 1/0 = 0, then 1 = 0*0.
Wait, if 1 / 0 = infinity, then infinity * 0 = 1 This seems just as bizarre, since zero times anything shouldn't become 1, no matter how big or how many times you do it.
According to the standard definition of division, 1/0 does not equal infinity. It doesn't equal anything. It is undefined.
Re: 1/0 = 0
#50Oh, so 0*0=1 ?
> So it is _not_ a theorem that a * (b / 0) = b * (a / 0)
As the article explains, the whole issue about dividing by 0 is the lack of multiplicative inverse. If you define division for 0 as something other than multiplication by the multiplicative inverse, there is no longer an issue doing the division. Hope that helps.