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references for consequences
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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. --[[User:Pdelong|Paul]] 16:13, 11 June 2007 (UTC)
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. --[[User:Pdelong|Paul]] 16:13, 11 June 2007 (UTC)

== 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

Revision as of 08:35, 3 July 2007

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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)[reply]

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)[reply]

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)[reply]

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)[reply]

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)[reply]

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