I read the differentiations between facts and opinions, and I either have doubts about them (which is unlikely), or I misunderstand them.
Is it a matter of understanding language definitions or philosophy?
My question is:
I read here that facts can be proven while opinions can't, but for example if I say: "It is hot!":
It can be proven whether I'm really hot or I'm lying by observing sweat. Then all opinions can be proven; So, there are no opinions.
It is also said that facts are universal while opinions are relative, but for example if I say "Earth is an irregularly shaped ellipsoid.":
Some people will say it is true, while some will say it is false and instead say that earth is flat. Then all facts can't be universal; So, there are no facts.
What is wrong with my claims? Do you use other definitions?