Appearance
Basic proof techniques
A proof is a finite sequence of steps which establishes the validity of a statement. When writing a proof, we assume the validity of a certain set of statements without proof (these statements are called axioms). So, roughly speaking, we start with a set of axioms (the most popular axioms in use is called Zermelo-Fraenkel (ZF) axioms), and apply a logical rule at each step, until we reach the desired statement; each such step is often called logical deduction.