[DrRocket]

BeuysVonTelekraft, on 17 November 2011 - 01:24 PM, said:

So, if there are lots of possible operations. How will i know what operation should i do?

A good surgeon will naturally pick the best operation.

Mathematicians work with the operation at hand, or invent one that provides insight in the situation that is presented. Quite often there are several operations available simultaneously, and the result is a richer algebraic structure , like a module, vector space or algebra. But in the case of a monoid one considers a very restrictive case, and only one operation is under consideration.

Where is it that you are encountering the concept of a monoid ? Quite typically one's first exposure to abstract algebra is via groups. There is much more that can be said about groups. If you have a particular text that you are reading, please tell us what it is. If not, I can recommend Michael Artin's Algebra.

[BeuysVonTelekraft]

DrRocket, on 17 November 2011 - 08:06 PM, said:

A good surgeon will naturally pick the best operation.

Mathematicians work with the operation at hand, or invent one that provides insight in the situation that is presented. Quite often there are several operations available simultaneously, and the result is a richer algebraic structure , like a module, vector space or algebra. But in the case of a monoid one considers a very restrictive case, and only one operation is under consideration.

Where is it that you are encountering the concept of a monoid ? Quite typically one's first exposure to abstract algebra is via groups. There is much more that can be said about groups. If you have a particular text that you are reading, please tell us what it is. If not, I can recommend Michael Artin's Algebra.

I am reading it here:


http://www.amazon.co...d/dp/3642001475