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My dictionary gives "integer" as > early 16th cent. (as an adjective meaning ‘entire, whole’): from Latin, ‘intact, whole,’ from in- (expressing negation) + th

My dictionary gives "integer" as > early 16th cent. (as an adjective meaning ‘entire, whole’): from Latin, ‘intact, whole,’ from in- (expressing negation) + the root of tangere ‘to touch.’ Compare with entire, also with integral,integrate, and integrity. Indeed, whole numbers is another word for integers, dated in English, but that's what they are called in some other languages like German and Russian. I also suspect natural is like in natural philosophy: occurring in nature, not like the other meaning of innate, although the two meanings are closely related. Imaginary is due to Descartes (https://en.wikipedia.org/wiki/Complex_number#History https://en.wikipedia.org/wiki/Complex_number#History): > [...] sometimes only imaginary, that is one can imagine as many as I said in each equation, but sometimes there exists no quantity that matches that which we imagine. It says Descartes didn't like them, but imaginary literally means not occurring in nature, and this was presumably before people accepted mathematical concepts as being as real as anything else. Transcendental also literally means beyond the algebraic numbers, since that's the definition, that's what they transcend. Surreal numbers are surreal because somebody (Conway?) needed to attach a prefix to real, and my dictionary says sur- is the same as super-. My dictionary says it is surreal that is the odd word here: a backformation for surrealism, which is some kind of art movement (I wouldn't trust some French painters to get English etymology right, eh? ;)). Also, what about dyadic, and p-adic, numbers? Ordinal numbers? Hyperreal?

agumonkey 10y ago
When you think about it, complex numbers are used to describe very natural properties, whereas natural, even though "naturally" simple, are very conceptual and symbolic.
sedachv 10y ago
> this was presumably before people accepted mathematical concepts as being as real as anything else Maybe as "unreal as anything else" would be a more accurate way to put it. Mathematical realism and even any kind of Platonism have a lot of detractors. I think the attitude change was more due to what is now known as Logicism (https://en.wikipedia.org/wiki/Logicism https://en.wikipedia.org/wiki/Logicism) and Formalism ( https://en.wikipedia.org/wiki/Formalism_(philosophy_of_mathematics) https://en.wikipedia.org/wiki/Formalism_(philosophy_of_mathe... ) when people realized that you did not need to appeal to the physical world to come up with useful things.
SilasX 10y ago
To add to this, "rational number" comes from "ratio" [2], not "rationality". They look similar because (per [1]) they both come from Latin ratio ("reckoning, accounting"), which derives from reri (think, judge). [1] http://www.dictionary.com/browse/ratio?s=t http://www.dictionary.com/browse/ratio?s=t [2] They're the numbers expressible as one integer divided by another.
- thefalcon 10y ago
  I realize not everyone is the same as myself, but I really wish that this etymology was explained when the concept of the rational number was introduced. I have trouble with rote memorization, but little trouble so long as I can derive a thing from first principles. Realizing that rational number comes from ratio seems so obvious in hindsight, but would have been so very helpful to my in-school self oh so long ago.
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  - lawpoop 10y ago
    When I took math in high school, our textbook had little blurbs that pointed out historical curiosities in regards to math. (The only one I remember clearly is an ancient Greek Queen? maybe Middle Ages, who did a lot of work on conic sections. So maybe it's not such an effective teaching tool since I didn't remember who exactly she was or when or where she lived). Anyway, all the people who said stuff like "When are we going to use X math topic in real life" were even more flummoxed by random math historical facts that weren't going to be on the test. Anyway, at least for me, I think I passed a point of maturity where I don't feel "bombarded" when I encounter additional information in regards to a math topic. I did poorly in math in high school, and, at the time, I felt that the less information, the better-- I could only integrate so much. But now at my age (almost 40) learning additional historical facts seems to help me understand the topic better.
schoen 10y ago
> but imaginary literally means not occurring in nature I would be tempted to say "pictured", "in a picture". https://en.wiktionary.org/wiki/imago#Latin https://en.wiktionary.org/wiki/imago#Latin But imago also has a lot of other meanings, and so "ghostly" and "conceptual" are also possibilities. :-)

agumonkey 10y ago

When you think about it, complex numbers are used to describe very natural properties, whereas natural, even though "naturally" simple, are very conceptual and symbolic.

sedachv 10y ago

> this was presumably before people accepted mathematical concepts as being as real as anything else Maybe as "unreal as anything else" would be a more accurate way to put it. Mathematical realism and even any kind of Platonism have a lot of detractors. I think the attitude change was more due to what is now known as Logicism (https://en.wikipedia.org/wiki/Logicism https://en.wikipedia.org/wiki/Logicism) and Formalism ( https://en.wikipedia.org/wiki/Formalism_(philosophy_of_mathematics) https://en.wikipedia.org/wiki/Formalism_(philosophy_of_mathe... ) when people realized that you did not need to appeal to the physical world to come up with useful things.

SilasX 10y ago

To add to this, "rational number" comes from "ratio" [2], not "rationality". They look similar because (per [1]) they both come from Latin ratio ("reckoning, accounting"), which derives from reri (think, judge). [1] http://www.dictionary.com/browse/ratio?s=t http://www.dictionary.com/browse/ratio?s=t [2] They're the numbers expressible as one integer divided by another.

thefalcon 10y ago
I realize not everyone is the same as myself, but I really wish that this etymology was explained when the concept of the rational number was introduced. I have trouble with rote memorization, but little trouble so long as I can derive a thing from first principles. Realizing that rational number comes from ratio seems so obvious in hindsight, but would have been so very helpful to my in-school self oh so long ago.
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- lawpoop 10y ago
  When I took math in high school, our textbook had little blurbs that pointed out historical curiosities in regards to math. (The only one I remember clearly is an ancient Greek Queen? maybe Middle Ages, who did a lot of work on conic sections. So maybe it's not such an effective teaching tool since I didn't remember who exactly she was or when or where she lived). Anyway, all the people who said stuff like "When are we going to use X math topic in real life" were even more flummoxed by random math historical facts that weren't going to be on the test. Anyway, at least for me, I think I passed a point of maturity where I don't feel "bombarded" when I encounter additional information in regards to a math topic. I did poorly in math in high school, and, at the time, I felt that the less information, the better-- I could only integrate so much. But now at my age (almost 40) learning additional historical facts seems to help me understand the topic better.

schoen 10y ago

> but imaginary literally means not occurring in nature I would be tempted to say "pictured", "in a picture". https://en.wiktionary.org/wiki/imago#Latin https://en.wiktionary.org/wiki/imago#Latin But imago also has a lot of other meanings, and so "ghostly" and "conceptual" are also possibilities. :-)