7.1

(First of all I would like to point out how stupid I am because I totally read 6.3 the other night, and spaced blogging about it. Dumb dumb dumb....)

1. What was the most difficult part of the reading for you?
Okay, I think I am understanding this idea... kind of... but I am really struggling with something pretty basic and silly: What the heck are the elements of this group? Like, in the main example they were using of functions mapping 1,2,3 to 1,2,3, so are the elements 1,2,3? or are the elements the mappings? I understand that the one operation was the "of" function, but what are the elements? If I had to guess, I'd guess that the elements are the mappings, but if that is the case, I think I'm mostly confused about what groups (in general) are or look like.

2. An 'axiom' summary of groups:
i) Closure under operation
ii) Operationally associative
iii) Identity element
iv) Inverse element for EACH element (whatever those are) of your Group.