4 ms·

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 multiplicati

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)

JadeNB 8y ago
> without multiplication and division being entirely symmetrical (as they already are not) What do you mean?
- deleted 8y ago
  [deleted]
- esrauch 8y ago
  Multiplication by x and division by x are inverses, except there is already the sole special case of x=0 where that isn't true. The common way to resolve that is and be consistent is to axiomatically decide: 1) there is no inverse of * 0 2) 0 is not part of the range permitted for 1/x The point of the article is that another way to resolve it and be consistent is to axiomatically decide: 1) there is no inverse of * 0 2) 0 is part of the range permitted for 1/x, and the resulting value is 0. As in, (x/y) * y=x is true either way only if y!=0. The only difference is whether when y=0 if it is not true because it is just illegal or if it is not true because (x/0) * 0 = 0 for all x.
  - JadeNB 8y ago
    > As in, (x/y) * y=x is true either way only if y!=0. The only difference is whether when y=0 if it is not true because it is just illegal or if it is not true because (x/0) * 0 = 0 for all x. Sure, I understand this claim. What I don't understand is the precise meaning of the claim "multiplication and division already are not entirely symmetrical." I don't know any existing technical meaning of "entirely symmetrical" for a pair of operations, but let's suppose that I switch the operations in your statement: > (x/y) * y = x is true [for all x] only if y != 0. Then I get: > (x * y)/y = x is true [for all x] only if y != 0. That's also true. What's the asymmetry?
hexane360 8y ago
Actually, that's the entire point of 0/0. It's indeterminate, meaning it can only take on a fixed value in the context of an operation to approach it (usually a limit).
EugeneOZ 8y ago
I kind of offended you personally or what? The entire point of this article is against the math and it means it's a bullshit.

JadeNB 8y ago

> without multiplication and division being entirely symmetrical (as they already are not) What do you mean?

deleted 8y ago
[deleted]
esrauch 8y ago
Multiplication by x and division by x are inverses, except there is already the sole special case of x=0 where that isn't true. The common way to resolve that is and be consistent is to axiomatically decide: 1) there is no inverse of * 0 2) 0 is not part of the range permitted for 1/x The point of the article is that another way to resolve it and be consistent is to axiomatically decide: 1) there is no inverse of * 0 2) 0 is part of the range permitted for 1/x, and the resulting value is 0. As in, (x/y) * y=x is true either way only if y!=0. The only difference is whether when y=0 if it is not true because it is just illegal or if it is not true because (x/0) * 0 = 0 for all x.
- JadeNB 8y ago
  > As in, (x/y) * y=x is true either way only if y!=0. The only difference is whether when y=0 if it is not true because it is just illegal or if it is not true because (x/0) * 0 = 0 for all x. Sure, I understand this claim. What I don't understand is the precise meaning of the claim "multiplication and division already are not entirely symmetrical." I don't know any existing technical meaning of "entirely symmetrical" for a pair of operations, but let's suppose that I switch the operations in your statement: > (x/y) * y = x is true [for all x] only if y != 0. Then I get: > (x * y)/y = x is true [for all x] only if y != 0. That's also true. What's the asymmetry?

hexane360 8y ago

Actually, that's the entire point of 0/0. It's indeterminate, meaning it can only take on a fixed value in the context of an operation to approach it (usually a limit).

EugeneOZ 8y ago

I kind of offended you personally or what? The entire point of this article is against the math and it means it's a bullshit.