1. proof and mathematical communication

1.1 a reminder of methods of proof (year 1)

  • x>7 can be written as {x : x > 7} and [7 , infinity)

  • disproof by counter example: using a counter example to disprove a statement,

  • proof by deduction: using what is given to reach a conclusion,

  • proof by exhaustion: using all possible situations for valid proof.

1.2 proof by contradiction

  1. you assume the opposite of what you are trying to prove e.g.,

    • prove there’s an infinite no. of prime numbers, assume there’s a finite no. of prime numbers where there’s a largest prime value.

  2. attempt to prove your assumption,

  3. locate contradiction and conclude.

1.3 criticising proof

  • finding errors in logic and arithmetic/algebra

  • such as the direction of arrows,

  • multiple solutions ± or only one solution

  • restrictions e.g., interval for degrees.