I don't get why commutative property is not valid under subtraction, because I find that it is for example: $5 - 3 = 2 = -3 + 5$ or rather $5 + (-3) = 2 = -3 + 5$ So how does it not hold true for negative numbers?
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1The example you wrote deals with commutativity for addition (of $5$ and $-3$). Why would subtraction be commutative? What sense does it make to ask "why" it is not? (whatever the sign of the numbers involved). That's life... – Anne Bauval Feb 21 '24 at 09:55
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1I changed the tag from commutative algebra to artihmetic because I don't think the "commutative algebra" tag is appropriate for this question – Eduardo Magalhães Feb 21 '24 at 09:59
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3Does this answer your question? How to explain to kid why subtraction is not commutative or any of those? Please next time use search engines (on this site and/or on the web) before (or instead of) asking. – Anne Bauval Feb 21 '24 at 10:03
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That is not the commutative property. If subtraction were commutative, what would mean that for any $a,b$; $$a - b = b - a$$ and this is clearly not the case, for example take $a=1$ and $b=2$
Eduardo Magalhães
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Addition is commutative: $$a+b=b+a$$ This holds for any numbers $a,b$, e.g. $a=5$ and $b=-3$, as in your example.
Subtraction is not (always) commutative: $$a-b\neq b-a$$ for most $a,b$ (not if $a=b$).
E.g. $5-3=2\neq-2=3-5$.
student91
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