Assume the opposite
Proof by contradiction starts with the opposite of the statement to be proved. A sequence of valid logical steps then leads to an impossibility, showing that this starting assumption cannot hold.
A contradiction is a clash between statements that cannot both be true. The proof must identify that clash, rather than simply assert that something has gone wrong.
1Assume
Begin with “Assume…” and state the opposite of the required result.
2Reason
Work through the consequences of this assumption using justified mathematical steps.
3Conclude
Identify the contradiction, reject the assumption and state that the required result follows.
The argument establishes the result by ruling out its opposite. Use short explanations alongside the algebra so that the reader can follow why the assumption fails.