State the Snake Lemma. Explain how to define the boundary map which appears in it, and check that it is well-defined. Derive the Mayer-Vietoris sequence from the Snake Lemma.

Given a chain complex $C$, let $A \subset C$ be the span of all elements in $C$ with grading greater than or equal to $n$, and let $B \subset C$ be the span of all elements in $C$ with grading less than $n$. Give a short exact sequence of chain complexes relating $A, B$, and $C$. What is the boundary map in the corresponding long exact sequence?