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Possible that I'm misunderstanding the concept of irrational numbers, but seems like the term nonrational would be much more clear. Why is "irrational" more clear than "nonrational"?

UPDATE: Just to be clear, it would be true to say the terms “irrational numbers” and “nonrational numbers” have the exact same meaning, and neither is something the other is not, correct?

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    Because to do so would be irrational.2012-08-27

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It is from Latin "irrationalis" ... so you have to blame those old Romans for this form.

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    Those bums didn't even speak English. :)2012-08-27
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There is also the fact that the prefix ir- is often (in English language) used for words which start with r, e.g. irreducible (which I don't think come from Latin), irregularity. Same way you have il- for words which start with l, e.g. illogical.

There are some discussion about this sort of things in English.SE e.g. 1, 2, 3.

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    See also [4](http://english.stackexchange.com/a/10725/77). The prefix _in-_ usually becomes _ir-_ before _r_, becomes _im-_ before _b,_ _m,_ or _p,_ and _il-_ before _l,_ a process known as sandhi/assimilation.2012-08-27
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The irrational numbers are the elements of $\mathbb{R}\backslash\mathbb{Q}$ , that is: the real numbers that are not rational.

This is not the same as non-rational since, for example, $i\in\mathbb{C}$ is not a rational number (since $i\not\in\mathbb{R}$ and in particular $i\not\in\mathbb{Q}$) so it is non-rational, but it is not an irrational number.

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    I'm with paul. Certainly in the context of Algebraic Number Theory and in Diophantine Analysis, $\sqrt{-1}$ is "an algebraic irrational".2012-08-26