12 different pairs of numbers with a difference of 12

Asked by maham237 @ 15/07/2021 in Mathematics viewed by 316 People

of numbers with a difference of 12 and that he had found them all. How would you respond to him?

Answered by maham237 @ 15/07/2021

Answer:

See explanation

Step-by-step 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

$12.5-0.5=12\\ \\13.4-1.4=12\\ \\12\dfrac{1}{8}-\dfrac{1}{8}=12\\...$

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.

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