Consider the closed interval $[0,1]$ and define $*$ on $[0,1]$ via $a*b=min[a,b]$. Determine whether $*$ is a binary operation on $[0,1]$.
No formal answer yet -- just throwing ideas around and need help with my scattered thoughts.
Since it is a closed interval $[0,1]$, the minimum for $a$ and $b$ would be $0,1$ as long as $a\neq b$?
Or is there something I am missing... Sorry, we started binary operations today so I am a little unsure on the concepts.
EDIT:
If its a closed interval $[0,1]$, any operation $a,b$ yields cannot be outside the interval(obviously?) Just putting together random thoughts. Again, sorry if its me just stating obvious, rudimentary things.