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I have the following sentence in a scientific paper.

“Here r, r1, and r2 are all not equal to zero.”

Does this mean that if one of them is zero, then the condition is not met? Or does it mean that at the same time they cannot be zero?

For example, is r=1, r1=2, and r2=0 a good input?

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    The operative word is "all". If any one of them is zero, then it not true that all of them are not zero. This is simply a question in Boolean logic, not in English. Jul 18 at 20:20
  • “Here r, r1, and r2 are all not equal to zero.” This is not a condition, it is a statement of fact: neither r, r1, nor r2 is equal to zero.
    – Greybeard
    Jul 18 at 22:59
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"all not equal to zero" means that r is not equal to zero, r1 is not equal to zero, and r3 is not equal to zero.

"not all equal to zero" means that at least one of them is nonzero, and the others could still be zero.

However, people do not always* obey this distinction. When you see a sentence like this you often have to guess the author's intent.

* (see the difference between "do not always" and "always do not"?)

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It is formally ambiguous.

In context, I believe it means that all of them are non-zero.

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  • It is not ambiguous at all. All not means none. Not all means no more than all.
    – randomhead
    Jul 18 at 22:40
  • We're talking about English, not logic. All that glisters is not gold was old when Shakespeare used it. And I don't know what you intend by no more than all, but sinxe more than all is incoherent, it doesn't seem to make sense.
    – Colin Fine
    Jul 19 at 12:58
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“Here r, r1, and r2 are all not equal to zero.”

Usually "not equal to zero" is found in math and science texts as "non-zero". As I read the sentence, it would be the same as and more clear as “Here r, r1, and r2 are all non-zero.”

All values are non-zero: r NOT EQUAL 0 r1 NOT EQUAL 0 r2 NOT EQUAL 0

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