Consider the following theorem:

The sum of two positive even integers is also a positive even integer.

What, if anything, is wrong with the following attempt at proving this theorem?

Proof.

Start by choosing the smallest two positive even integers, 2 and 2. 2 + 2 = 4, which is also even. Then try 2 + 4 = 6, which is also even. Then 2 + 10, 2 + 12, etc., all of which add up to even totals. Then try adding 4 + 4 = 8, 4 + 6 = 10, and so on. All the resulting sums, for any two pairs of positive even integers, add up to an even integer. Therefore, the sum of two positive even integers is also a positive even integer.

Question

Consider the following theorem: 
 
 The sum of two positive even integers is also a positive even integer.

What, if anything, is wrong with the following attempt at proving this theorem? 
 
 Proof. 
 
 Start by choosing the smallest two positive even integers, 2 and 2. 2 + 2 = 4, which is also even. Then try 2 + 4 = 6, which is also even. Then 2 + 10, 2 + 12, etc., all of which add up to even totals. Then try adding 4 + 4 = 8, 4 + 6 = 10, and so on. All the resulting sums, for any two pairs of positive even integers, add up to an even integer. Therefore, the sum of two positive even integers is also a positive even integer.

Answer

The proof does not follow logically, because the theorem is not true.

Answer

The proof is not verifiable, because there are an infinite number of sums that need to be evaluated in order to verify it.

Answer

There is nothing wrong with the proof.

Answer

The proof is not verifiable, because it is impossible to verify the result of each individual sum.

Answer

The final sentence does not follow as a logical consequence of the previous statement.

Crowdly

Consider the following theorem: The sum of two positive even integers is als...

Want instant access to all verified answers on learning.monash.edu?