A lot of people gave good responses. I think the best answer is that it depends on context. There are good reasons why it should be undefined, 1 or 0 depending on what you’re doing with it. Most people accept that it is 1, sometimes it makes more sense to be undefined or 0.
For an example for it to be 1, consider a combination lock on a briefcase. It has 4 digits, and each digit has 10 possible values. So there are 10^4 = 10,000 combinations. (Imagine the dials go from 0-9, so you have combos 0000-9999)
Now imagine the briefcase has no lock. How many ways can you can you arrange nothing? Just once.
The possible ways to arrange no objects in no possible ways is ∅ (empty set). So we have one possibility, empty set.
A lot of people gave good responses. I think the best answer is that it depends on context. There are good reasons why it should be undefined, 1 or 0 depending on what you’re doing with it. Most people accept that it is 1, sometimes it makes more sense to be undefined or 0.
For an example for it to be 1, consider a combination lock on a briefcase. It has 4 digits, and each digit has 10 possible values. So there are 10^4 = 10,000 combinations. (Imagine the dials go from 0-9, so you have combos 0000-9999)
Now imagine the briefcase has no lock. How many ways can you can you arrange nothing? Just once.
The possible ways to arrange no objects in no possible ways is ∅ (empty set). So we have one possibility, empty set.