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Why is it that subtraction is noncommutative but addition of a negative number is? Everything I can read says that subtraction can be view as adding a negative. However, when you view it in this way the noncommutative property of subtraction is broken. Therefore can they not be considered equivalent?

An example: Subtracting two numbers $$ 2-3= -1 $$ $$ 3-2 =1 $$ Viewing it as adding a negative $$ 2+(-3)=-1 $$ $$ (-3)+2=-1 $$ Therefore upon viewing it as adding a negative one of the principal parts of subtraction is broken.

Eric Wofsey
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James Kervin
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1 Answers1

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To view subtraction as addition with negatives we must change the sign of the second number and after we do that we can rearrange the order. But the number which sign is changed must be the second number and never the first. If we change the order of subtraction it wouldn't be the second number that changes sign. Once it becomes addition we can rearrange the numbers any way we want. But we can't rearrange the numbers before it becomes addition.

fleablood
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