2024-03-01 10:32 UTC
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..
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@SmartmanApps@dotnet.social 2024-03-01 10:33
6/6 So no, there is nothing arbitrary about the order of operations rules at all - they are a natural consequence of the way we have defined things (such as multiplication is defined as a shorthand form of addition, and so has to be done first). So there's nothing arbitrary in Maths, 1+1=2 everywhere, and having different Physics or a different base doesn't mean we have different Maths. Maths is universal, only the notation for it varies by region.