- #1

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- Homework Statement
- What does these symbols mean?

- Relevant Equations
- ##f : R \rightarrow R##

I was studying mathematical logic and came across this statement of

I'm having a hard time in understanding it. I have concluded that ##G## is any set but not an empty one, ##\circ## is a function having input as two variables (both variables are from set ##G##) and gives just one output (which is also in ##G##) and there exists an element ##e## in ##G##.

But I'm not able to understand the axioms, what does ##x~~\circ~~(y\circ z) ## means? In above notation ##\circ## is a function and from some previous knowledge I know that ##g\circ f## means ##g(f(x))##, so are those ##x,y~ \textrm{and}~ z## functions? but why we have that ##\circ## between them? What is it trying to convey?

Thank you. Any help will be much appreciated

**group theory**I'm having a hard time in understanding it. I have concluded that ##G## is any set but not an empty one, ##\circ## is a function having input as two variables (both variables are from set ##G##) and gives just one output (which is also in ##G##) and there exists an element ##e## in ##G##.

But I'm not able to understand the axioms, what does ##x~~\circ~~(y\circ z) ## means? In above notation ##\circ## is a function and from some previous knowledge I know that ##g\circ f## means ##g(f(x))##, so are those ##x,y~ \textrm{and}~ z## functions? but why we have that ##\circ## between them? What is it trying to convey?

Thank you. Any help will be much appreciated