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What is a sensible, correct and non-ambiguous way of rephrasing the following?

The numbers a, b and c are not simultaneously positive, negative nor even.

The idea is that the three numbers are not all three positive, they are not all three negative and they are not all three even. Saying it like this is too repetitive, but the first option is silly because it can also be read as saying that each of the numbers is not positive, negative and even at the same time.

This is for a research math paper, by the way. Note that a, b and c are not really numbers for us to apply special properties. They are called numbers merely for illustration here.

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  • @Jasper, I am simplifying: the three objects are not even numbers, and the three properties they do not have have nothing to do with positivity, &c. This is a rather technical text I am writing! Jun 15 '12 at 22:12
  • @Mariano can you provide an example more closely related to what you are trying to say? Do the three objects really even have states? Jun 15 '12 at 22:20
  • The objects have properties, rather than states. I sensible rephrasing of the example I gave in the question would be indicative enough for me, @cornbreadninja: as I wrote, the actual context of the paper is complicated. Jun 15 '12 at 22:27
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a, b and c are not all positive, not all negative, and not all even.

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The numbers a, b and c are neither all positive, nor all negative, nor all even.

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  • I always feel something's amiss when I use neither with more than two alternatives :) Jun 16 '12 at 6:47
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    @Mariano - Fowler's Modern English Usage mentions that when used as an adverb, neither should only have two options. However, it also has this to say. "... This restriction to two does not hold for the adverb (neither fish nor flesh nor fowl)."
    – user16269
    Jun 16 '12 at 9:05
  • I found it interesting to see how various translators handled this issue when translating this Bible passage into English. The majority seemed to have no problem exercising their right to string nors together, but a couple have included some extra neithers, apparently reluctant to use more than one nor per neither.
    – J.R.
    Jun 16 '12 at 9:50
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    I mistyped my earlier comment. I meant to write that Fowler "... mentions that when used as a pronoun, neither should only have two options ...". Sorry.
    – user16269
    Jun 16 '12 at 10:16
  • @David, yup, I know: it still feels wrong for some reason. Thanks for the reference, btw. Jun 16 '12 at 18:36
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I kind of think your original sentence is already good enough. However, I prefer this even more:

The numbers a, b and c are not all positive, negative or even.

All really removes the ambiguity you worry about.

In any case, due to the presence of nor, the misreading one is positive, one is negative, and one is even is not likely. To have that reading, it will be worded more like not simultaneously positive, negative and even.

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  • A never would be odd, because the objects do not ever change, though. Jun 15 '12 at 22:35
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Sometime a bulleted list works well to convey such easily-tangled information:

The numbers a, b and c are not:

  • simultaneously positive (e.g., 2, 11, 14), or
  • simultaneously negative (e.g., -1, -2, -3), or
  • simultaneously even (e.g. -4, 0, 2)

This eliminates some of the potential repetition, and allows you to easily furnish an example to reinforce what you are talking about.

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"The numbers a, b and c are not all positive, nor are they all negative or all even."

or

"The numbers a, b and c are not all positive, neither are they all negative nor even."

or

"The numbers a, b and c are not all positive, they are also all neither negative nor even."

Although I might change the order to have positive and negative at the end as they are opposites of each other.

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