The fact that there’s no buckets means that you can’t then usefully draw any further conclusions about the ratio of buckets to things. In your first two examples we can take the results and use them to work out further things like how much might the buckets weigh, what happens if we add more buckets or more things, etc.
In the divide by zero answer, we know nothing about the buckets, and the number of things becomes meaningless. But worse of all is that it’s easy to hide this from the unwary, which is why you occasionally see “proofs” online that 1=2, which rely on hiding divide-by-zero operations behind some sneaky algebra.
When we say we “can’t” divide by zero, we mean ok you can divide by zero, but you’ll get a useless answer that leaves you at a mathematical dead end. Infinity isn’t reversible, or even strictly equal to itself.
I think I get it, thanks for taking the time to explain.
With 10/2 there are two buckets, and 10/1 there is 1, so with 10/0 I was wrong to phrase it as there is a ‘bucket with nothing in it’, it should be ‘there is no bucket, so you can’t put anything in the bucket, even if you wanted to.’ Right?
The fact that there’s no buckets means that you can’t then usefully draw any further conclusions about the ratio of buckets to things. In your first two examples we can take the results and use them to work out further things like how much might the buckets weigh, what happens if we add more buckets or more things, etc.
In the divide by zero answer, we know nothing about the buckets, and the number of things becomes meaningless. But worse of all is that it’s easy to hide this from the unwary, which is why you occasionally see “proofs” online that 1=2, which rely on hiding divide-by-zero operations behind some sneaky algebra.
When we say we “can’t” divide by zero, we mean ok you can divide by zero, but you’ll get a useless answer that leaves you at a mathematical dead end. Infinity isn’t reversible, or even strictly equal to itself.
I think I get it, thanks for taking the time to explain.
With 10/2 there are two buckets, and 10/1 there is 1, so with 10/0 I was wrong to phrase it as there is a ‘bucket with nothing in it’, it should be ‘there is no bucket, so you can’t put anything in the bucket, even if you wanted to.’ Right?