Talk:Abstract Algebra/Group Theory/Group/Definition of a Group/Definition of Identity

=Intent of Illustrating Different Usage of the Theorem= Panick2k4, thank you for your edits. Here is your revision:


 * Definition of Identity is: $$ \exists \; e_{G} \in G: \forall \; g \in G: e_{G} \ast g = g \ast e_{G} = g $$
 * It means, e is the identity of group G, because:
 * 0. There is at least one eG belonging to group G, such that,
 * 1. for every element g in group G,
 * 2. eG $$\ast$$ g = g $$\ast$$ eG = g

It is grammatically sound and flows well in terms of English. However, it does not illustrate the different usage of the theorem in the subsequent theorems in this section. I am sorry that I did not made the intent to show different usages of the theorem clear enough in the original version. Your corrections of grammar is much appreciated. Arydye001 (talk) 22:43, 24 July 2010 (UTC)


 * I will not pursue the issue further since you are the one working on the book but consider that by reinterpreting the statement:
 * Definition of Identity is: $$ \exists \; e_{G} \in G: \forall \; g \in G: e_{G} \ast g = g \ast e_{G} = g $$
 * in a by step way as it is now it creates an unnecessary inequality between the mathematical statement and the interpretation.
 * It should be read:
 * Definition of Identity is: There exists a $$e_{G}$$ belonging to G, such that for any g member of G, in a binary operation it will have the commutative property ($$ e_{G} \ast g = g \ast e_{G} $$) and be neutral ($$ e_{G} \ast g = g ; g \ast e_{G} = g $$).
 * The unnecessary complexity created between the first and the second was what lead me to attempt to correct it. Take this as a constructive criticism on the present situation. My view is that it could be made easier to understand and more mathematically correct in the translation of the symbols... --Panic (talk) 23:27, 24 July 2010 (UTC)




 * May be it can look like a step by step interpretation to some people, but that is not my intention. Do you have some suggestions of improving this aspect while still allow the article to show the different usages of the definition?


 * I want readers to understand the different usage of the definition. People might confuse different usage of the definition, just like the different usage of a word in English.


 * This kind of confusion is like confusing the meanings of "see" in "I see", which means understands, and in "I see a black cat", which means perceives through vision.


 * To avoid this kind of confusion, some dictionaries list different usage of the same word. Similarly, I think listing different usage of the same definition can help our readers.


 * Some of the links from other theorems to this page has (usage x) to indicate which interpretation of the definition is the proof using, as the same definition can have more than one meaning Arydye001 (talk) 00:44, 25 July 2010 (UTC)


 * I did read it as a badly stated step by step interpretation, one solution is to reverse the presentation, start by your simplification and then provide the mathematical statement. Use notes for clarification that don't have a direct impact on the on topic information.
 * You should also increase wikilinks and interlinking between the book pages even if something seems obvious to you. I did come across this page because I was reviewing something and wasn't fallowing the meaning of binary operation, then I decided to correct that and it lead to editing this page. --Panic (talk) 00:55, 25 July 2010 (UTC)


 * I remember that I liked the link to binary operation added by you.. I am sorry that I forget to add it back. Arydye001 (talk) 01:11, 25 July 2010 (UTC)


 * You can create a different template for the book. Duplicate/Create a Note template in Template:Abstract Algebra/Note and configure it for use in the book. Remember to add to the page also, if you evolve from the original make a entry on the original template talk just to let know that you will be using it a bit afferently.   --Panic (talk) 03:35, 25 July 2010 (UTC)