# Using none for three or more nos. in mathematics

Which form is correct?

None of A,B or C divides X

or

None of A,B and C divides X

• I'd say they're both "acceptable", but personally I'd prefer or rather than and. Note that some people will be happy with Neither A nor B nor C works, but others will reject this on the grounds that neither/either only work with two alternatives. Apr 13, 2018 at 14:31
• Do we say: "A, B or C divides X", where A, B and C are numbers? Apr 13, 2018 at 14:44
• @FumbleFingers That was not my question. My question is: Do we say in the English language that: 2,3, 4 divides 12?? Or do we usually say: 12 is divisible by 2, 3 and 4. (I was not addressing the the word or.) And none of x seems really wrong to me. Apr 13, 2018 at 14:54
• I don't know. A few minutes spent thinking about this and looking around on the web have got me nowhere. I guess that to me the two alternatives in the original question both seem grammatical but a bit unnatural. Apr 13, 2018 at 15:30
• In standard mathematical English, the expression is: X is not divisible by A, B and C. Nov 1, 2021 at 17:16

Let's get real. [joke]

There are many shortcuts or tricks that allow you to test whether a number, or dividend, is divisible by a given divisor. This page focuses on the most-frequently studied divisibility rules which involve divisibility by 2, 3, 4, 5, 6, 8, 9, 10, and by 11

arithmetic

Finally, none of refers to a portion of something. Numbers here are not portions. They are whole numbers.

• 12 cannot be divided by 5, 10 or 3.

We would never say in English: None of 5, 10 or 3 etc.

Why? Because it would imply that 5 can be broken down into portions. It can't. It can only be rewritten with other whole numbers: 2+ 2+1 is 5.

AS IN: None of the pie or pies were left after the party. The guests had eaten the whole thing or all of them.

• "None" here would simply refer to the portion of the listed items, not that any of the individual items can be broken into portions. I don't see any real difference between "None of these numbers are divisible by 2", "None of them are divisible by 2", and "None of 3, 5, or 7 are divisible by 2." You can pretty much always replace a pronoun ("None of them") with the noun(s) it represents ("None of 3, 5, or 7"). Nov 1, 2021 at 17:51
• @NuclearHoagie No, it would not. For that to be the case, linguistically, it would have to say: None of these numbers (3, 5 or 7) are divisors of 12. None of 3, 5 or 7 [big fat buzzer]. None of the numbers in the set [OK] Nov 1, 2021 at 17:55
• None of the numbers in the list; None of the numbers given to you etc. Just like you can't do this: None of Jerry, Louise or Martin were on the bus. Nov 1, 2021 at 17:56
• I cannot imagine any situation where a sentence could be ungrammatical with a noun ("None of [3, 5, or 7] are divisible by 2") , but grammatical when directly substituting a pronoun instead ("None of [them] are divisible by 2"). Pronoun substitution changes absolutely nothing about a sentence's grammatical structure. Nov 1, 2021 at 18:15
• @NuclearHoagie It's not the pronoun. It's the compound subject. See my post. None of does not work with a compound subject sentence. None of sheep, hamsters, or rabbits are carnivores. That is ungrammatical but None of them are carnivores is grammatical. None of only works to differentiate between members of a group, not between groups themselves. We use a different structure to differentiate multiple subjects. Sheep, hamsters, and rabbits are not carnivores. No need for none. Nov 1, 2021 at 18:20

Neither form is desirable. They are hard to understand. Generally starting a sentence with None of and then iterating a list of items to which None of applies is cumbersome. For example, None of my kids, Carol's kids, or Lester's kids swim well. If none of them swim well you don't need to specifically call out the none. I will understand that from context.

My kids, Carol's kids, and Lester's kids do not swim well.

That means none swim well.

A, B, and C do not divide X.

Once again that means none. No reason to say it.

For sentences with a single subject none of works very well.

None of our kids swim well.

None of those numbers divide X.

It's when you add the itemized list to none of that things start getting cumbersome.