Simple Proof Methods: Tips

• If you use new symbols or notation of your own, always explain what it stands for. Example: Instead of writing:
  Suppose that $n \in \mathbb{Z^+}$.write:Let $\mathbb{Z^+}$ (

  $\mathbb{Z^+}$

  ) denote the set of positive integers, and suppose that $n \in \mathbb{Z^+}$.
• Use symbols from fixed categories properly. The lowercase letters $a, b, c, d, e$ are used for constants; the letters $f, g, h$ are used for function names; the letters $i, j, k, l, m, n, o$ are used for integers; the letters $p, q, r, s, t$ are used for rational numbers or propositions; the letters $u, v, w, x, y, z$ are used for real numbers; uppercase letters $A, B, C$, are used for containers such as sets, sequences, etc.
  Example: Instead of writing:
  We have $f \in a$.write:We have $x \in A$.