Wikipedia:Reference desk/Archives/Mathematics/2014 October 12

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October 12

Usage of articles in math English

Should I write "if x and y are positive then a number z=x+y is positive" or rather, "if x and y are positive then the number z=x+y is positive"? On one hand, this z appears anew, it was not introduced before. On the other hand, given x and y, there exists only one z defined by that phrase. Boris Tsirelson (talk) 18:11, 12 October 2014 (UTC)

i am no more — Preceding unsigned comment added by 86.152.102.224 (talk) 18:14, 12 October 2014 (UTC)

Using the lost grammatical adage "when in doubt, rephrase", I'd use "if x and y are positive then z=x+y is positive". But it forced to pick from one of the two choices I vote for the second one. --RDBury (talk) 18:57, 12 October 2014 (UTC)

Thank you. Yes, I feel forced to choose, since really I write more complicated texts :-) such as "...then the/a function f defined by...satisfies..." (and instead of "function" it could be a longer noun group, like "separable reflexive Banach space" etc). Or do you think I can always rephrase? How? Really, I also feel more comfortable writing "the", but I got unsure, being confused by opposite opinions, like this: but when you introduce me someone, you say "a friend of mine" even though he is uniquely defined, if not by your words then by your gestures. Boris Tsirelson (talk) 19:54, 12 October 2014 (UTC)

It may sound strange, but I don't mind if slightly different styles (as long as they are "correct") are used in a longer text. It can help avoiding monotonic repetition, of which there is plenty anyway in mathematical texts. But in the present case, the second option gets my vote too. YohanN7 (talk) 20:49, 12 October 2014 (UTC)

Thank you. Having vote 2:0 (or even 3:0, counting myself) I get more sure. No, I do not find it strange... I also like some variations; but I face this case quite often. But wait, do you say that these "a" and "the" are both correct, or not? Boris Tsirelson (talk) 20:57, 12 October 2014 (UTC)

I'm not a native English speaker (I'm Swedish), but I'd say, as a guess, that both options are correct, but the first option seems unusual, it doesn't seem to fit. Perhaps it would fit in a bigger example with more ingredients. YohanN7 (talk) 21:07, 12 October 2014 (UTC)

It depends a bit on how you "read it out loud inside your head" when reading. An equation like z = x+y can "be pronounced differently" when given a context. YohanN7 (talk) 21:17, 12 October 2014 (UTC)

The Language Reference Desk may be a better place to post this question. As a native English speaker I am sure that it should be the and not a, because as you said there exists only one z defined by that phrase. --catslash (talk) 23:18, 12 October 2014 (UTC)

Thank you; if you are sure, also I am. Yes, I understand it is a language question; but sometimes math jargon differs from usual English. Boris Tsirelson (talk) 05:57, 13 October 2014 (UTC)

It should be "the". Compare:

• "This is a friend of mine" / "x+y is a number".
• "The friend of mine that I introduced earlier is smart" / "The number x+y is positive".

In the first version, there is only one "this" to whom I'm pointing, and only one number "x+y". But that's the first part of the sentence. In the second part, I have many friends and there are many numbers, hence "a friend" and "a number".

In the second version, there is only one friend that I introduced earlier, and only one number x+y. Hence "The friend that..." and "The number x+y...". -- Meni Rosenfeld (talk) 09:03, 14 October 2014 (UTC)

Matrices being sets of vectors?

A vector as you might already know is basically a 1xn or nx1 matrix. It defines a position in a particular number of dimensions.

Can matrices be used to define an n-dimensional shape and where it is in n dimensions?

Like for example would the matrix:

[1 2 1 2 2 1 1 2]

[1 2 2 1 2 1 2 1]

[1 2 2 2 1 2 1 1]

define a 1x1x1 cube in 3D space? Caters1 (talk) 18:53, 12 October 2014 (UTC)

While one certainly could do it, the question of under what circumstances one should do it or whether people actually do do it are the better questions. If you can find a standard matrix operation, e.g. matrix multiplication, determinants etc., which does something useful if you express a problem using a matrix then I'd say have at it, that's how new applications of matrices are invented. If matrix operations don't do anything useful then I'd say don't create unneeded jargon.--RDBury (talk) 19:24, 12 October 2014 (UTC)

There are instances where rows or columns actually are vectors, or interpreted as vectors. The determinant and matrix diagonalization comes to mind - and the operator matrix in linear transformation. This matches the title of the thread, but not your actual question. YohanN7 (talk) 19:37, 12 October 2014 (UTC)