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I know that for two numbers x and y, relationships like x < y (and x <= y sometimes) are called inequalities. Note here, there is an order between x and y, for example (3 < 5).

But what's the correct usage to express the relationship that two numbers are merely not equal to each other, i.e. x <> y?

Do we also call this an "inequality" (could be confusing) or do we call this something else?

I tried to use unequality, and spell checkers always tell me it's wrong.

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    "These two numbers are equal".... "These two numbers are unequal"...
    – Marv Mills
    Dec 7 '15 at 14:36
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    This might be a better fit for the math section of SE. Dec 7 '15 at 14:39
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    Unequal, not equal, not the same, different.... (And spell checker is only there as an assist. Use a dictionary to check the spelling of words you're unsure of.)
    – Hot Licks
    Dec 7 '15 at 14:41
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    (How is "inequality" confusing?)
    – Hot Licks
    Dec 7 '15 at 14:43
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    Have you looked up 'inequality' and 'unequal'? Dec 7 '15 at 17:15
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The term you are looking for is inequality.

The Merriam Webster Dictionary defines inequality as:

1 the quality of being unequal or uneven... Middle English inequalite, from Latin inaequalitat-, inaequalitas, from inaequalis unequal, from in- + aequalis equal First Known Use: 15th century

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  • Doesn't quite fit the OP; "express the relationship that two numbers are merely not equal to each other"... 'The values 7 and 23 are ______", though I suppose you could say "7 and 23 have inequality", but it seems a bit clunky...
    – Marv Mills
    Dec 7 '15 at 14:48
  • @MarvMills - Where does the OP say "The values 7 and 23 are ______"?
    – Hot Licks
    Dec 7 '15 at 15:57
  • @HotLicks Clearly the OP does not- it is practical example of a sentence using the form the OP does imply, showing that the suggestion in this answer would not work as well. I am sure you knew that.
    – Marv Mills
    Dec 7 '15 at 16:27
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    @MarvMills - So, why don't you answer the question?
    – Hot Licks
    Dec 7 '15 at 16:38
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    @HotLicks why don't you? This line of questioning is off-topic and pointless. I'm out.
    – Marv Mills
    Dec 7 '15 at 16:40
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In mathematics, it is common to say that two numbers are distinct.

x and y are distinct integers.

x, y, and z are (pairwise) distinct integers.

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  • What about 'unequal'?
    – Mitch
    Dec 7 '15 at 18:04
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Some mathematicians and computer scientists have tried to introduce "disequality" to mean a statement that two numbers (or other entities) are distinct. As far as I can tell, this suggestion is not catching on.

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