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If $xy > 0$, then $x$ and $y$ are [insert fancy smart term for same sign]

Does "sign parity" work here?

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17  
... then $x$ and $y$ have the same sign. Why complicate things? –  Mariano Suárez-Alvarez Mar 30 '12 at 4:46
4  
I have seen $xy \gt 0$ being used to denote that they have the same sign! –  Aryabhata Mar 30 '12 at 4:47
6  
Why do you need a fancy smart term? Just say they have the same sign. –  Qiaochu Yuan Mar 30 '12 at 4:50
11  
Doing artificial things to try and "look smart" usually only works on people who are clueless about the material. On everybody else, it tends to have exactly the opposite effect. –  Hurkyl Mar 30 '12 at 5:26
4  
"either both positive or both negative"...Anyhow the best way to look smart on a HW is by keeping thing neat, SIMPLE, and making no mistakes ;) –  N. S. Mar 30 '12 at 5:39

2 Answers 2

up vote 12 down vote accepted

A quick search in Google Books gives the following quote:

[..] Hence, if $\Delta_{r-1}$ and $\Delta_r$ are of opposite signs, $\Delta_{r+1}$ and $\Delta_{r+2}$ are of the same sign as $\Delta_r$ [..]

You can't be smarter than H. S. M. Coxeter!

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1  
It even rhymes! –  Bruno Joyal Mar 30 '12 at 5:59
    
Yes, but what did Gauss use? –  Alex Becker Mar 30 '12 at 6:05
    
...or you could say they are "of like sign"... –  J. M. Apr 3 '12 at 17:38

If $x$ and $y$ are real numbers, then the followings are equivalent.

  • $xy>0$.
  • $x$ and $y$ are both nonzero, and cannot have differing signs.
  • The closed line segment connecting $x$ and $y$ does not contain $0$.
  • One can go from $x$ to $y$ without ever touching $0$.
  • The intervals $[x,y]$ and $[-x,-y]$ have no common point.
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