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”)