Talk:Fixed point (mathematics)

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[edit] fixed point of "f(x) = x + 1"

The claim that "f(x) = x + 1" has no fixed point in the reals implies that there is a complex number for which it does have a fixed point. There isn't one, is there? I mean, assuming that we restrict ourselves to numbers and the normal interpretation of "=" and "+", x+1 has no fixed points, right? —Preceding unsigned comment added by 129.173.155.95 (talk • contribs)

It does not imply that. There are other things besides reals and complex numbers to which addition of 1 may be done. Transfinite cardinals, for example. Michael Hardy 28 June 2005 20:17 (UTC)
Also, when using IEEE 754 floating point numbers ("doubles"), repeatedly adding 1 to any non-integer value (or an integer between -2^52 and +2^53) eventually converges on the integer 2^53. So you could say that (one) fixed point of "f(x) = x + 1" is x=2^53. --70.189.77.59 04:07, 15 October 2006 (UTC)
No. Unless you think 253 is not an element of the additive group of integers, you can't say that. The fact that \pm 2^{53} + 1 = \pm 2^{53} when you're using IEEE 754 is caused by rounding errors. --Tinctorius 10:01, 30 April 2007 (UTC)
True, but there is no common example besides transfinite numbers. If you want construct a group in which x + 1 = x holds, then 1 would be the identity element of addition, which is commonly called 0. --Tinctorius 10:01, 30 April 2007 (UTC)

[edit] Image

The image used in this article is of the function sin(x), which is rather confusing given that the text next to it is about cos(x). It should probably be changed. Quendus 12:51, 15 October 2006 (UTC)

I'm trying to make a cosine version, but somehow my version of Gnuplot sucks at making SVGs. Maybe someone might want to rebuild it using the included source code. --Tinctorius 10:01, 30 April 2007 (UTC)
Done. Nice abstraction there. –EdC 23:22, 30 April 2007 (UTC)


[edit] Eigenvectors

Fixed points seem to be deeply related to eigenvectors. I added "Eigenvector" to the "See also" section, but perhaps a mathematician could go into more detail? —Ben FrantzDale 23:25, 26 September 2007 (UTC)