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

Does "sign parity" work here?

  • 0
    I've never heard anyone use the phrase, "sign parity".2012-03-30
  • 1
    That's because I made it up lol...2012-03-30
  • 18
    ... then $x$ and $y$ have the same sign. Why complicate things?2012-03-30
  • 4
    I have seen $xy \gt 0$ being used to denote that they have the same sign!2012-03-30
  • 6
    Why do you need a fancy smart term? Just say they have the same sign.2012-03-30
  • 0
    Because I want to look smart on my HW...2012-03-30
  • 0
    There are plenty of other ways to accomplish that goal. I second @Aryabhata's suggestion, though.2012-03-30
  • 1
    If you just absolutely have to have an english term for this, I would use "have matching signs." Though $xy > 0$ seems better to me...2012-03-30
  • 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.2012-03-30
  • 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 ;)2012-03-30
  • 0
    I find it legitime (and common) to introduce nouns to denote something as fixed-term property. For instance x "is positive" after fiddling many times with "x has positive sign". Another instance x and y "are correlated" in a text, where the according observation of how their values jointly behave was discussed. (This is just the power of abstractions). A natural candidate for some noun/adjective for two numbers having the same sign would be "are like-signed", or "are same-signed". (But that's surely not much creative at the moment...)2012-03-30
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    While I agree with most of the comments made so far that there is no fancy commonly accepted term for this relation, and as a general principle it's best not to complicate things, I do think the OP has asked a perfectly reasonable question. There might have been a non-obvious standard term after all, and to communicate efficiently it is good to learn standard terminology. After all, there are non-obvious 'fancy' terms in mathematics which the eager student of mathematics might like to familiarise him/herself with. For example...2012-04-05
  • 0
    ...$b^2-4ac$ is called the discriminant of $ax^2+bx+c$, though I personally didn't know this till after I'd seen hundreds of quadratics.2012-04-05

3 Answers 3

12

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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    It even rhymes!2012-03-30
  • 0
    Yes, but what did Gauss use?2012-03-30
  • 0
    ...or you could say they are "of like sign"...2012-04-03
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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.
0

I agree with user2468. Usually this is stated $x$ and $y$ have the same sign. sgn($x$)=sgn($y$) could also be used. [Weisstein, Eric W. "Sign." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Sign.html]

Also "sign parity" would be confusing since "parity" is used to refer to even or oddness.