1.4 A: Proof

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Question 41

A technician monitoring a high-precision chemical reaction states that the temperature, $T$ in $∘C^\circ C$ , must satisfy the constraint $54.4 < T < 54.5$ . The technician claims that $54.5$ is the largest possible temperature within this specification.

Explain the error in the technician's statement.

[1]

bi.

A research scientist argues that there is no largest value for $T$ in the interval $54.4 < T < 54.5$ and provides the following proof by contradiction:

Step 1: Assume there is a largest temperature in the interval $54.4 < T < 54.5$ and let this largest value be $L$ .

Step 2: Let $\frac{L + 54.5}{2}$ .

Step 3: $L < k < 54.5$ , which is a contradiction.

Step 4: Therefore, there is no largest temperature in the interval $54.4 < T < 54.5$ .

Explain the contradiction stated in Step 3.

[1]

bii.

Using a similar method, prove that there is no smallest value of $T$ in the interval $54.4 < T < 54.5$ .

[3]

1.4 A: Proof

Question 41

Explain the error in the technician's statement.

[1]

bi.

A research scientist argues that there is no largest value for $T$ in the interval $54.4 < T < 54.5$ and provides the following proof by contradiction:

Step 1: Assume there is a largest temperature in the interval $54.4 < T < 54.5$ and let this largest value be $L$ .

Step 2: Let $\frac{L + 54.5}{2}$ .

Step 3: $L < k < 54.5$ , which is a contradiction.

Step 4: Therefore, there is no largest temperature in the interval $54.4 < T < 54.5$ .

Explain the contradiction stated in Step 3.

[1]

bii.

Using a similar method, prove that there is no smallest value of $T$ in the interval $54.4 < T < 54.5$ .

[3]

1.4 A: Proof

Question 41

1.4 A: Proof Questions

1.4 A: Proof

Question 41

1.4 A: Proof Questions