Talk:Image (mathematics)

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Mathematics Portal This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.
Mathematics rating:	Start Class	Mid Priority	Field: Foundations, logic, and set theory
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Needs significant expansion, especially the vital role of images in abstract algebra (via the isomorphism theorems for instance). It's possible to create a fork to image (abstract algebra), but some systematic treatment is essential for the project. (If progress is made, please alter my comment accordingly.) Silly rabbit 15:51, 30 May 2007 (UTC) Needs to be kept separate from Range —Preceding unsigned comment added by 71.55.23.120 (talk) 01:02, 5 October 2007 (UTC)

The epsilon signs don't show up for me (show up as boxes)

You need a better browser (or default font). We should probably include a link to {{SpecialChars}} on this page. -- Fropuff 21:45, 8 December 2005 (UTC)

[edit] Image and graph

Using the set names given at the beginning of this articles, do all elements of the set Y ordered with all elements of the set X make up the graph of the function f? --Abdull 15:46, 31 May 2006 (UTC)

I'm not sure what you mean by "all elements of the set Y ordered with all elements of the set X". Do you mean X x Y, that is the set of all ordered pairs (x, y) such that x is an element of X, and y is an element of Y? IIn any case, that is not the graph of f. The graph of f is the set of all pairs (x, f(x)) such that x is an element of the domain of f. Thus the graph of f is a subset of X x Y, (in fact it is a subset of X x f[X]). Paul August ☎ 16:08, 31 May 2006 (UTC)

[edit] Image for image

I think that an illustration would be very helpful in describing this concept. Below is an image that I made for this article. I used terminology not used in the article however. Silly Rabbit, could you tell me what variables you want me to replace in the image. Thanks--Cronholm144 05:18, 31 May 2007 (UTC)

[edit] references for consequences

Does anyone know of any references for the identities listed in the "consequences" section? Deriving the first four identities is an exercise in a book I'm reading, and I'm able to correctly demonstrate all but the second. I can only show that it's an equality, but that's apparently wrong. If anyone knows where I can find its derivation, please update the references section, or include the derivation here in the talk section. Thanks. --Paul 16:13, 11 June 2007 (UTC)

Consider the following counterexample for why it is not an equality. Let f=x^2 and let E_1=[0,inf), let E_2=(-inf,0]. The intersection of f(E_1) with f(E_2) is [0, inf). The image of f(E_1 intersect with E_2) is {0}. You should be able to use this example to pinpoint why any attempt at a proof for the equality will fail. —Preceding unsigned comment added by 202.36.179.66 (talk) 01:47, 10 June 2008 (UTC)

[edit] inverse and image

It seems that the inverse image of a function and the image of the inverse of a function is written the same way. Very confusing