Question

Explain whether it is always true that a difference between two numbers is smaller than either of the numbers. Give an example to justify your answer.

Answer 1

If you find the difference of say a positive number minus a negative number the result is not smaller.
for example
\[5 - (-3) = 8; 8 > 5 or -3. False claim\]
so it is incorrect to say that the difference is always smaller then either of the numbers
Furthermore:
if you can see the point, the "difference" is merely a subtraction from the first number by the second, but if the second number has a negative value then it creates an increase an effect similar to adding two numbers

Answer 2

That's a good question and a great answer, but it seems out of place in the linear algebra study group.