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I have been looking for several translations for words such as "integer" and "decimal number" (A number with digits past the decimal point), and I realized that there don't seem to be translations for such words.

For integer, I took the approach of the German language, "ganze Zahl" (meaning whole/complete number), and translated it as mI' naQ.

For "decimal number", I found that Klingon does have a translation for decimal point, vI’. I believe it would be possible to say the equivalent of "number with decimal point", but I'm not sure how to structure that.

Are there simpler or better ways to translate these? What about for things like rational numbers, irrational numbers? One other thing I was wondering is if there were some way to say a number is positive or negative?

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    I would not try to duplicate the term rational/irrational in Klingon -- irrational (as well as terms like imaginary) arose for historical reasons that are unlikely to have existed in Klingon history. Would the Klingon have had the equivalent of Roman numerals prior to decimals? Do they have a base 10 system? What do Chinese or Arab or Indian mathematicians call irrational numbers? Maybe investigating non-Western mathematical history can guide us in coming up with Klingon terms for these concepts. – Jeff Jun 16 '18 at 7:48
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    Klingons do use base 10. that being said given the Klingon history its quite likely that the majority of their maths & science is inherited from the Hurq and other alien civilisations meaning that etymology is probably not a reliable approach here. – Ummdustry Jun 16 '18 at 7:57
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    This question may be a better fit for Constructed Languages – Stop Harming Monica Jun 16 '18 at 10:17
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    Just guessing: rational & irrational --> honourable & dishonourable. – Gaultheria Jun 18 '18 at 21:23
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    There is only one type of Klingon number: the type that counts how many enemies you have slaughtered today! Klingon mathematicians killed all the other types of numbers. – Paul D. Waite Jun 19 '18 at 13:41
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Word of Okrand

The closest thing to that that I’m aware of is an article by Mark Okrand in the March 1996 issue of HolQeD: The Journal of the Klingon Language Institute. Unfortunately, that doesn’t appear to be available any more, even as a back issue in paper form, but it is summarized here.

The Klingon words for arithmetic operations are derived from boq (which means either add or ally). Multiplication is boq'egh, literally ally with oneself. The suffix -Ha' means undo and seems to indicate the inverse of an operation. So, boqHa' means subtract and boqHa''egh means divide. The result of this operation takes the verb chen, literally, “forms.” The example of division would be wejlogh boqHa''egh jav; chen cha', for "six divided by 3 makes two" or, hyper-literally, "thrice, six undoes multiplication; two forms."

Even and Odd Numbers

The two types of numbers we do have official translations of are mI' mob, meaning odd number (literally "number alone"), and mI` mobHa, meaning even number (literally "number not-alone").

Fractions

Okrand did not (that I know of) say how to talk about fractions. The only fraction words we know about appear to be irregular: cha' is two, cha'Dich means second, and bID means half. However, valth means hundred, vI' means decimal point, and vatlhvI' means percent. It is possible that -vI' is some kind of productive suffix for naming fractions, with bID being an irregular form, so that hypothetically * chorghvI' would mean one-eighth. The evidence for that extrapolation is not very strong, but it would be consistent with what little we know.

The Field of Rational Numbers

My best guess for how to translate “rational numbers” would be boqHa''eghlaHchuq Hoch mI'mey, literally "all the numbers can divide each other." The rational numbers are the smallest superset of the integers with this property. A good stab at how to refer to a generalized field might be to replace number with a word meaning element or member (tuqnIgh?). This is a reasonable shorthand for the definition of a field. Group and ring elements might be described as being able to subtract and multiply each other, respectively. We could also make a relative clause or verbal noun out of this, like “numbers that divide each other,” but from the examples we’ve been given, this does not seem to be the normal Klingon usage.

An alternative: the metaphor for arithmetic is that multiplication is allying with yourself, and division disassociating with yourself. So Klingon might extend It. A rational number is one formed by a number breaking an alliance with itself, so it might be a mI' par'egh (number that dislikes itself), and an irrational number would be a mI` parHa''egh (one that does not dislike itself).

I’d be interested to hear whether any Klingonists have talked about this already.

Other Sets of Numbers

The official Klingon vocabulary does have words for continuous quantities, much as ancient Greek mathematics did: lengths and areas. (It also has words for coordinate and radio frequency that might easily have related mathematical meanings.)

In particular, 'ab means to have the width or height of something, so we might describe real numbers as those that measure distances (or some other continuous quantity).

Although this might be too close to English usage, Klingon has words for square and cube, so we might literally say “associates with itself to form a square” or “forms a square,” and then square root might be, literally, to measure the width or height of a square ('ab meyrI`). Then we might refer to the algebraic integers as the numbers that can measure the sides of squares ('ab'laH meyrImey').

An alternative is that ghoS means to follow a course, proceed and ghoSchoH indicates an instantaneous change of position or course. So that might be a good way to refer to a derivative. Limits might be a form of paw, meaning arrive, perhaps pawchoH, "in the process of arriving at a definite objective." Either might be a plausible etymology for a definition of the real numbers like the ones in use by twenty-first-century mathematicians on Earth.

Another form of ghoS is ghoSqa`, to follow a course, stopping and restarting. This could be a good way to refer to discrete or discontinuous functions. Discrete sets might vi'qa', accumulate by stopping and restarting. This has the double meaning of sharpshooting, which might be a natural analogy for set comprehension.

For what we call the imaginary numbers, we would need to get creative. We know a Klingon word for firing a projectile, baH. Since He means a course or route, baHHe might mean the trajectory of a ballistic projectile. A ballistic trajectory is (approximately) a parabola, whose equation is quadratic. Factorizing this equation might be something like, baHHe lagh, to take apart the path of a missile. And the roots of a generalized quadratic equation are the complex numbers. Therefore, the Klingon phrase for complex numbers might, hypothetically, be, "can take apart the path of a missile" (baHHe laghlaH).

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