Question about Mathematics from Zamiatin.

[Terry Moran]

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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