What is proof?

• Proof is the process of showing something is true in every case, often by using algebra

Given an algebraic expression…

1. Expand brackets
2. Simplify (work with left-hand side only if = sign involved)
3. Make sure you finish with the statement you are proving

Given just words…

• This is a bit trickier but turning it into algebra is usually the best thing to do

4. Give things names (use as few letters as possible):

• • n?is “any integer” (or?m?or?k?or…)
  • n + 1?is the integer after?n?(“consecutive”)
  • 2n?is an even integer (2n + 2?is the next one)
  • 2m?is a different even integer
  • 2n + 1?is an odd integer (and?2n + 3 is the next one)

5. Then go on as above (“Given an Algebraic Expression”)