Final answer:
Alec is incorrect because the sum of two numbers can be less than either number, especially with negative numbers. For example, the sum of -5 and 3 is -2, which is less than 3. The commutative property of addition (A + B = B + A) does not influence whether the sum is less than any of the addends.
Step-by-step explanation:
Alec's statement that the sum of two numbers can never be less than either number is incorrect because in mathematics, particularly when dealing with negative numbers, the sum can indeed be less than either original number. To model this, let's use the numbers -5 and 3. When we calculate -5 + 3, the sum is -2, which is less than 3.
The property that Alec refers to, A + B = B + A, demonstrates the commutative property of addition, which means that the order in which two numbers are added does not affect the sum. This is true for both positive and negative numbers alike.
Another part of the question seems to mention the addition of fractions as well as probabilities and entropy, but these sections are a bit out of context and do not directly illustrate Alec's misconception. It's important to note that rules of mathematics, like 12 + 19 = 31, are universally valid irrespective of location or time period, and the sum equals 31 whether the addends are counted in goats or students.