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how would you call the relation like this? $$\ln(\sqrt{5})<\ln(5^2)$$ Is it inequality or inequation?

Motivation for this question: In Czech we have different words for a relation involving equality sign and a problem involving equality sign and a variable and the value of the variable is to be found. To the best of my knowledge, the same is in English: equality and equation.

Further, in Czech we have the same concept also for relations including $\leq$ and $\geq$ signs. In English I have never heard the word inequation till yesterday :). To the best of my knowledge
$$\ln(\sqrt{5})<\ln(5^2)$$ (a statement) and $$\ln(x+2)<\ln(5^2)$$ (problem to isolate $x$ such that the relation is true) are both called inequalities in English spoken by mathematicians (conferences, papers, ...).

But a friend pointed me to the existing word inequation, which (at least according to Wikipedia) really exists. Is this word common in math English? Is it possible and common to use this word for the relations above? Or does it mean just $\neq$, as Mathworld states?

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  • $\begingroup$ see wiki, maybe help some: en.wikipedia.org/wiki/Inequation $\endgroup$
    – J. Yu
    Mar 8, 2016 at 9:32
  • $\begingroup$ Thanks, I have seen. This does not tell me, whether people really use this word. I work many years in the field, have seen many English textbooks on similar topics and never found this word. $\endgroup$ Mar 8, 2016 at 9:40
  • $\begingroup$ Notice, that $\ln\left(5^2\right)=2\ln(5)$ $\endgroup$ Mar 8, 2016 at 9:41
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    $\begingroup$ Personally, I do not use inequation. Given that mathworld.wolfram.com/Inequation.html defines it using $\not =$ while Wikipedia uses $\lt$, there may be insufficient use to make the meaning clear unless the user defines the intended meaning each time $\endgroup$
    – Henry
    Mar 8, 2016 at 9:43
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    $\begingroup$ As a native speaker in the U.S. who is in physics graduate studies, this is the first time I've ever heard "inequation." I would say then that it is extremely uncommon. I'd refer to all of your statements as inequalities. $\endgroup$
    – zahbaz
    Mar 8, 2016 at 10:16

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Although English is not my native language, I'm quite familiar with most mathematical terms used in English. I have never used the word "inequation", nor have I read or heard it. I might add that the word "inequation" is not that useful (that is, not necessary), since "inequality" is widely known, and used for the same purpose. Since this has been discussed in the comments, let me adress this too: as wikipedia states:

Some authors apply the term only to inequations in which the inequality relation is, specifically, not-equal-to ($\neq$).

So it seems to depend on the author what is meant by inequation, but I'm sure you can get this out of the context.

Conclusion is, I'd recommend just using "inequality", but the opinions are different from person to person. Just make sure you understand what someone means by it when he uses "inequation" or "inequality", and figure out what you like best (after all, being consequent with your usage makes reading/listening easier).

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Inequality is a characteristic (or quality) that an inequation possesses. I realize that inequality is commonly used to denote a mathematical assertion that two things are not equal, but that usage has always grated upon my sense of grammaticality. Use inequation!

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