I have to prove that $\mathbb{R}$ is a field. One of the properties for $\mathbb{R}$ to be a field is that addition in $\mathbb{R}$ is associative. I wanted to use this property as an example for the other ones.
My question is, how can I show something so intuitive? Can I say that it is simply assumed that addition in $\mathbb{R}$ is associative? Or should I use $a+(b+c)=(a+b)+c$ for $a,b,c \in \mathbb{R}$ in some way?
I am sorry for the silly question, it has been a while since I proved something. Thank you.