While I am reading the wikipedia page of Homology and Reduced-homology groups, I've ran into following equation.
$H_0(X) = \tilde H_0(K)\oplus\Bbb Z $
For given X, which is defined to be simplical complex a priori, $H_0(X)$ defines the free abelian group with the connected components of X as generators, which means if there's a given simplical complex, $H_0(X)$ fills out that boundary to be solid. This is what I understood.
Now, back to our equation, especially the LHS, then there's a reduced form with the notation tilde and $\Bbb Z$, what does $\oplus$ refer to?
Any hint to proceed my understanding?
And If the proof is given, the following would be much more helpful to understand what the equal signs means.