Question

Your friend said that there are exactly 12 different pairs of numbers with a difference of 12 and that he had found them all. How would you respond to him?

Answer 1

See explanation

Explanation:

I wouls say to my friend that he is incorrect, because there are infinitely many pairs of numbers with a difference of 12.

For example,

`13-1=12\\ 14-2=12\\15-3=12\\16-4=12\\...`

Here we can increase the first and the second number by 1 and get their difference equal to 12 after this operation.

The same is possible with negative numbers:

`-1-(-13)=12\\ -2-(-14)=12\\-3-(-15)=12\\ ...`

Actuall, we can do this with decimals too

`12.5-0.5=12\\ \\13.4-1.4=12\\ \\12(1)/(8)-(1)/(8)=12\\...`

Such pairs of numbers are infinitely many (because there are infinitely many real numbers) and we cannot find all possible numbers with difference of 12.