2024-03-01 10:27 UTC
4/6
I've also seen people claim that some things in Maths are "arbitrary", like the order of operations rules. e.g. they try to say that multiplication ONLY comes before addition because "we chose that", and that, according to them, we could "choose" to make it the other way around. I debunked that already at https://dotnet.social/@SmartmanApps/111243269757880043 but in short the rules are a natural consequence of the way we have defined things. e.g. 2x3 is short for 2+2+2. So now imagine an expression like 2+3x4...
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@SmartmanApps@dotnet.social 2024-03-01 10:32
5/6 3x4 is short for 3+3+3+3, which is equal to 12, so 2+3x4=2+12=14, so the order of operations rules have to make sure we get 14. So if "we chose" to make addition first, as some claim we can. Well, 2+3x4=5x4=5+5+5+5=20, which isn't 14, so it's wrong! And that's because multiplication is shorthand for addition, so we have to expose the hidden additions before we do addition. This rule is a natural consequence of the definition of multiplication as being shorthand for addition..