For sets $A$, $B$, and $C$, why is $A\times B\times C$ is not the same as $(A\times B)\times C$. I have an intuitive sense as to why the associative law does not apply here, but can someone provide me with a more concrete reason as to why it doesn't? Thanks!
Fill in more details in: .... because $(1,2,3)$ has only one set of $()$ while $((1,2),3)$ has two sets of $()$. So they can't possibly be the same.
For finite sets $A, B$ and $C$, since there exists a isomorphism between $A\times B\times C$ and $(A\times B)\times C$, probably the only difference is the notation. But things change when some of them are infinite.