301.2 Definition of a Group

A group is (in a sense) the simplest structure in which we can do the familiar tasks associated with "algebra." First, in this video, we review the definition of a group.

[PunmasterSTP]

Set of nouns? More like "Super lectures where learning abounds!" 👍

[NeillClift]

Thanks for these videos. Very useful. In your identity statement you say that for all g in G there is an h in g. But g is an element. So you need to say there is an h in G

[eukleidesk]

Since you didn’t specify as part of the definition that identity elements are unique, doesn’t the inverse in the third part depend upon which identity element you’re referring to? I realize there will, ultimately, be only one identity “e” but it seems to me that, a priori, there might be more than one. I suppose, since we can show there is only one identity without referring to the existence of inverses, it doesn’t matter whether inverses are assumed to exist with respect to all, or just some, identity element. (If I am confused, I apologize.)