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1/0 = 1(±∞) https://twitter.com/westurner/status/960508624849244160 > How many times does zero go into any number? Infinity. [...] > How many times does zero go into zero? infinity^2?
Zero goes into zero x times, for any real x. Infinity isn't real, therefore neither is infinity^2 so no.
What value does 1/x approach?
What about 2/x?
And then, what about ∞/x? What value would we expect that to approach? ∞(±∞)
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.
You know.. dividing is like breaking something up [..]
Oh, 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)
This article grinds my gears. He quotes a number of mathematicians that correctly state the undefined nature of 1/0. Then proceeds to interpret that this means that we can choose any specific value to represent as 1/0 that we want. NO. We have "NaN" for a reason and it is an important signal to the programmer that a mistake was made. The language that assigns it to 0 silently is bunk as is this article.
Erm, when we say it's "undefined" we mean it literally -- standard mathematical systems of arithmetic do not define a value for that division.
If you make another system of arithmetic you can define it how you want and be consistent with "regular maths" for the operations in which things are defined. It's an extension.
> We have "NaN" for a reason
Funnily enough, IEEE754 defines 1/0 as positive infinity, not Nan. But none of these things are "the truth" in any reasonable sense of the word, just "useful systems".
Defining it as 0 at least means floating point numbers are (presumably) closed under arithmetic operations, which could be handy.
Earlier 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.
Earlier quoted context omitted.
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'…
Zero is not a very good NaN.
a=x/N
b=y/N
If a==b, then x==y
No longer true, with this change. Essentially a variety of mathematical properties of numbers in the Real space don't hold when you allow division by 0.
Given a/b = c, your intuition of finding c is to get a number such that c×b = a.
c×0 = 0 has an infinite number of solutions, 0 being a particularly practical one.
c×0 = 1 (and more generally a≠0) has no solution, especially in the reduced explanation of multiplication as taking integer multiples of a value.
(Also note that having 0/0 = 0 maintains symmetry and continuity of the function y = 0/x.)
The Post JavaScript Apocalypse https://youtu.be/99Zacm7SsWQ?t=2434
The limit of x/y as x and y go to zero depends on which path across the xy plane you take towards the singularity. Along one approach, the limit is 0, along another approach the limit diverges to infinity, along yet another the limit is 17.
I'm not kidding! Go to https://www.geogebra.org/3d and enter "x/y" and spin the graph around. The "value" at x=0 y=0 is the entirety of the z-axis.
For another perspective, try http://www.wolframalpha.com/input/?i=z%3Dx%2Fy and turn on contour mode for the 3D plot. Notice how the contour lines radiate out from the z-axis; each of those is an "approach" to the singularity at a different z-value, and taking the limit along each line leads to a different value.