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Why subtracting a negative same as adding positive and adding a negative same as subtracting a positive why.i didn't get the logic why subtracting 2-(-3)=5. Pls give me a logical answer

dxiv
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user1051200
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    Would you rather I remove a debt of three dollars or would you rather I just give you three dollars? You come out the same either way. If I give you 2 dollars and also remove a debt of 3 dollars, it’s the same as if I’d simply given you 5 dollars. – littleO May 31 '22 at 03:51

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There is some deep theory behind this, but here is the rundown:

  • -3 is what is known as the 'additive inverse' of 3 (basically the opposite)
  • Subtraction is just the inverse (opposite) of addition
  • The inverse of an inverse of something is the original thing (think of a double negation, like "I am not not going to the park" = "I am going to the park")
  • a-b is the same as a+(-b)
  • So, 2-(-3)=2+(-(-3))=2+3=5

I hope this helps :D

gmod
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    Not sure what deep theory you’re referring to. We can give a common sense explanation (“removing a debt”) or we can give a short proof from the axioms. Either way, there’s nothing deep or scary. – littleO May 31 '22 at 05:37