Question about Mathematics from Zamiatin.

[R. M. Cleminson]

The Russian textbook, as so often, is wrong: "ratio" in this context does not mean "reason", but "ratio", and (as someone in this discussion has already stated) a rational number is one that can be expressed as a fraction (i.e. the ratio between two whole numbers), whereas an irrational number cannot.  (This all goes back to ancient Greek mathematics.)  Nevertheless, a false etymology is also a cultural datum...

----- Pôvodná správa -----
Od: "Alexandra Smith" <Alexandra.Smith at ED.AC.UK>
Komu: SEELANGS at LISTSERV.UA.EDU
Odoslané: nedeľa, 8. december 2013 12:23:19
Predmet: Re: [SEELANGS] Question about Mathematics from Zamiatin.

Dear Terry,

A similar explanation in Russian is given here, so you could check the  
terminology used in Russian textbooks on mathematics:  
http://numbers.kalan.cc/irrational.php

And here: http://school.xvatit.com/index.php?title=Иррациональные_числа
The latter explains why the word "irrational" is being used to signify  
smth. that is opposite of something that is rational: "Прежде всего  
заметим, что в математике не принято говорить «нерациональное число»,  
обычно используют термин иррациональное число. Термины «рациональное  
число», «иррациональное число» происходят от латинского слова ratio —  
«разум» (буквальный перевод: «рациональное число — разумное число»,  
«иррациональное число — неразумное число»; впрочем, так говорят и в  
реальной жизни: «он поступил рационально» — это значит, что он  
поступил разумно; «так действовать нерационально» — это значит, что  
так действовать неразумно)."



All best,
Alexandra


Quoting Terry Moran <t.moran at NEW.OXON.ORG> on Sun, 8 Dec 2013 10:48:04 +0100:

> A note on imaginary / complex and irrational / transcendental numbers.
>
> If we place real numbers on the horizontal axis (1, 2 etc. going right, -1,
> -2 etc. going left), then the vertical axis (intersecting with it at zero
> on both axes) represents *imaginary numbers:* i, 2i etc. going up, -i, -2i
> etc. going down. i is the symbol arbitrarily assigned to the square root of
> minus 1, obviously imaginary because no real number gives minus 1 when
> multiplied by itself. Any point located on the plane formed by these two
> axes but not actually on either of them is called a *complex *number: i +
> 4, -7 - 3i for example, in the north-east and south-west quadrants
> respectively.
>
> Irrational numbers have numerical expansions that never end and never
> repeat. Examples are pi (3.14159...), e (2.71828...) and the square root of
> 2 (1.41421...), but these aren't all the same: some irrational numbers are
> also *transcendental*, which means they're not the root of a polynomial
> equation. The square root of
> 2<http://en.wikipedia.org/wiki/Square_root_of_2> is
> irrational but not transcendental, since it's a solution of the polynomial
> equation x2 - 2 = 0. There are no polynomial equations to which the
> solution is pi or e, so they're transcendental as well. There are lots of
> others.
>
> Russian uses the same terms: мнимые / комплексные and иррациональные /
> трансцендентные числа. I assumed the Russian for *real numbers* would
> be реальные числа, but on checking I find it's вещественные числа.
>
> I'm open to correction on both the maths and the language!
>
> Terry Moran
>
>
> On 7 December 2013 18:46, Anthony Anemone <AnemoneA at newschool.edu> wrote:
>
>> Dear colleagues,
>>
>> I'm puzzled about Zamaitin's usage of иррациональный when referring to the
>> square root of -1.  As far as I understand math terminology in English (not
>> that far!), wouldn't that be an imaginary number?  Perhaps terminology in
>> Russian is different?
>>
>> Thanks!
>>
>> Tony
>> --
>> Tony Anemone
>> Associate Professor
>> The New School
>> 72 Fifth Ave, 702
>> New York, NY 10011
>>
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