Talk:Bijection
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In this page it is said that When X and Y are both the real line R, then a bijective function f: R → R can be visualized as one whose graph is intersected exactly once by any horizontal line.
For intuitively sound functions this is probably true.
However, consider the function <math>f: R -> R<math> with
<math>f(x) = 2x<math> for every <math>x \in Q<math> and
<math>f(x) = -2x<math> for every <math>x \in R-Q<math>.
For this example it is ofcourse still true that for every <math>y \in R<math> there is one unique x with the property that <math>f(x)=y<math>. But it is not any longer possible to give a clear visualisation of this, in the way described in this page.
Regards, Bob v. R.
merge
I think we should merge this page with injective function and surjection. They are already using the same pictures. Any objections? What should be the name of the new page? MarSch 16:36, 21 Apr 2005 (UTC)
- That's a tough one. Maybe properties of functions? Deco 04:44, 22 Apr 2005 (UTC)
- Yes, I was thinking maybe it could simply be jection or injection, surjection and bijection or
in-, sur- and bijection or maybe injective, surjective and bijective or then again in-, sur- and bijective. Jection or maybe jective would make linking easy: injective, although it doesn't highlight as I expected/hoped. Maybe I should file that as a bug. -MarSch 12:42, 22 Apr 2005 (UTC)
- Let's not make article titles that are meaningless on their own. The linking feature as it is now is useful for links like noncommutative, although I can't say I've seen such a link recently. Deco 16:42, 22 Apr 2005 (UTC)