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.
Explain 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.
368 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division. Each one has a worked solution and a mark scheme showing where the marks go.