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What is the difference between, say, 10 and 2?
Seems obvious to me. 10-2=8. The difference is 8.
What is the difference between 2 and 10?
Seems obvious to me, at first, i.e, 8 again. But then I’m wondering why I shouldn’t be calculating 2-10=-8 this time, given that the 2 appears first in the question this time.
Q. Can you have a difference of -8? Can you have a difference of negative anything?
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When I Googled it I was pointed to the number line.
When I then wrote out the 1 to 10 section of the number line, and circled 2 and 10, it showed that there were 7 numbers in between them (3 4 5 6 7 8 9).
This puzzled me further.
Any thoughts?
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Depends on whether the sign means anything in the context of what the numbers represent.
E.g., if I owe you $10, then my balance with you is -10. Now I repay you $2, so +2 - 10 = -8, my new balance with you.
Other examples might be like comparing how far the two of us walk. Do we care about just the absolute value, or care whether you go North (+) and I go South (-) ?
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What is the difference between, say, 10 and 2?
You discovered already 3 possible solutions (perhaps there are more). This is math's work, and you did it well.
But you will also know the right one when you know to what 10 and 2 refer in real.
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Depends on whether the sign means anything in the context of what the numbers represent.
E.g., if I owe you $10, then my balance with you is -10. Now I repay you $2, so +2 - 10 = -8, my new balance with you.
Other examples might be like comparing how far the two of us walk. Do we care about just the absolute value, or care whether you go North (+) and I go South (-) ?
Thanks, Phil.
No context was given in the original question. It was a proof question, about the difference of the squares of 2 consecutive integers. I used the difference between 2 and 10 for the sake of simplicity.
I get your points about absolute value etc, but what if nothing like that is stated. What if someone merely asks for the difference between 2 and 10?
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Thanks, KerimF
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