Most numbers are plural, except one, which is singular –
there’s only one.

However, there’s also lots of zeroes – who knows how
many, but it is a plural, like all the other numbers except
one. For example: four cactii; three cactii; two cactii;
one
cactus; zero cactii.

I think it would
be a good idea for science to actually
count the zeroes, then we’d know how plural it is. Once
we’ve counted them, we could simply substitute all the
plural zeroes with the standard reference zero,
which equates to any zero at all. Then we could count
zero
properly as if it is not more than a one, like two is.

It’d probably have to be kept under glass, in France
somewhere, and measured periodically.

I have a strong suspicion, [Ian], that the plural of cactus is
cacti. Only one "i". Personally, I find that this error (or,
perhaps misdirection) calls into question an otherwise sound
proposal.

I might also point out that the rule is not universally
applicable. Bananas and potatoes are counterexamples, as
everyone knows. <link><link>

We have never seen a cactus with any sort of optical sensing organ. On the other hand, potatoes are reknowned for having multiple eyes, as many as eight being far from uncommon. This suggests that potatoes and spiders are related, which means that either potatoes are arthropods, or spiders are in fact a type of vegetable tuber.

Zero cacti is a mirage anyway. It actually fits the definition of an "imaginary" number, because somewhere between 0.00001 cactus and zero cacti, it disappears completely (on this side of the universe anyway!) Functionally there's no difference between zero potatoes and zero cacti, except in imaginary taste.

Makes me wonder that in a row of planted potatoes and one is missing, is that a zero potato or a negative potato? Clearly, because it should be there, it is a negative potato but also, technically, it is a zero potato.

It would probably depend on if it was originally there or not.

You could also infer that a negative potato would be a NOT potato, which implies everything that is not a potato, including the set of all not potatoes itself.

No, because it's not divisible by 1. Prime numbers are integers having only two factors, 1 and the number itself (Sieve of Erastothenes).

Also, all prime numbers are odd; 3, 5, 7, 11. Since any even number is divisible by two, and any even number which has two subtracted from it is also even, and 2 - 2 = 0, zero is an even number and therefore cannot be prime.

//Functionally there's no difference between zero potatoes and zero cacti//

Au contraire. In Ireland, the continued presence of zero cacti throughout its history was, & continues to be, of no consequence whatever*. But a sudden outbreak of zero potatoes (potati?) was a catastrophe.

*I am ignoring the presence of houseplants in this context because I want to. I am sure they are irrelevant but I can't be bothered to prove it with facts.

//Functionally there's no difference between zero potatoes and zero cacti, except in imaginary taste.//

We can, therefore, prove that potatoes and cacti are the same:

Potatos are /items/, and so are cacti. Whether they are of different /types/ is to be seen.
Let us suppose that we have a group of N items of the same type.
If we remove an item from the group, we have a group of N - 1 items, all of the same type. If we add another item of the same type as those in the group, we have another group of N items. By our previous assumption, all the items are of the same type in this new group, since it is a group of N items.
Thus we have constructed two groups of N items all of the same type, with N - 1 items in common. Since these two groups have some items in common, the two groups must be of the same type as each other.
Therefore, combining all the items used, we have a group of N + 1 items of the same type.
Thus if any N items are all the same type, any N + 1 items are the same type.
This is clearly true for N = 1 (i.e. one item is a group where all the items are the same type). Thus, by induction, N items are the same type for any positive integer N. i.e. all items are the same type.

//it would be a good idea for science to actually count
the zeroes,

That's easy, weigh a hard disk, take off the cover then
set it for max revs for a bit. Then weigh the disk again
, all the 1's will have been centrifuged out, leaving
just the zeros.

Thinking on this some more, it's about environment. Origin and zero are two different things. A zero potato is a volume of soil whereas a negative potato is a volume of soil with a void equal to a potato.

Would it be true to say that if there is zero potato
in the soil, then, providing there’s room in the soil
for such potential, there’s more than one zero
potati, or, if plural, potatii (just as there must
have been more than one Pompei in Roman times).
Hencethus, you could also say there are zero
potatoes, indicating with a sweep of the gesture, a
whole raft of no potatoes where there might have
been.

Since potatoes aren't buoyant, that would float better than a raft of actual potatoes. The voids where potatoes could be, but aren't, when filled with air, would float quite well.

Since quantum stuff is constantly popping in and
out of existence and neutrinos are everywhere, can
we really say that zero actually exists as nothing?
And what does it mean to say that 'nothing' exists?

Where's one of those philosophy majors when we
actually need them?

You've made a mistake somewhere up there. I can tell you with
absolute certainty that there's a difference between zero potatoes and
zero spiders. Given a choice of which to eat, I'm taking the zero
spiders every time. Give me any number of potatoes, zero or non-
zero, but the spiders on my plate had darn well better be the zero of
them.

If you multiply zero by an uncountably infinite
number, like the cardinality of the set of transcendental
numbers, for
instance, is the result still zero? Is it a different result
than multiplying it by the cardinality of the set of all natural
numbers?
Does the power of zero get exhausted after strictly
enforcing that much ado about nothing?

So, let's say the value of aleph 1, or perhaps w+1, multiplied
by zero. Would that result in aleph null? I don't want to
break math, just bend it a little and see if it snaps back.