I am a university student, professor gave us definitions of Borel algebra and Borel σ-algebra. In Wikipedia they are the same see here.
but professor defined Borel algebra as: let $\Omega$ be $[a,b)$ set on real line. Borel algebra on $\Omega$ is finite intersection of such $[c1,c2), [c1,c2], (c1,c2], (c1,c2)$ intervals.(in wikipedia it is not finite it is countable, please help me which one is correct). are in fact Borel algebra and Borel σ-algebra same? please give me real definitions.