A student claims that 7 is the largest value of mmm in the interval 6<m<76 < m < 76<m<7.
Explain the error in the student's statement.
A teacher states that there is no largest value of mmm in the interval 6<m<76 < m < 76<m<7 and provides the following proof by contradiction:
Step 1: Assume there is a largest number in the interval 6<m<76 < m < 76<m<7 and let this largest number be LLL.
Step 2: Let n=L+72n = \frac{L + 7}{2}n=2L+7.
Step 3: L<n<7L < n < 7L<n<7, which is a contradiction.
Step 4: Therefore, there is no largest number in the interval 6<m<76 < m < 76<m<7. \nExplain\nExplain\nExplain the contradiction stated in Step 3.
Using a similar method, prove that there is no smallest value of mmm in the interval 6<m<76 < m < 76<m<7.
Practise AQA A Level Maths 1.4 A: Proof with exam-style questions for A Level Maths. 107 questions covering 1.4.1 Structure and methods of proof, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
