this post was submitted on 19 Jul 2023
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In your example you lose distributivity. (2+4)2 is 22+4*2, which doesn't matter for numbers but it matters for algebra. If addition comes first then there's no way to represent distribution.
The distributive law, assuming commutativity and other axioms, is a*(b+c) = (a*b) + (a*c). Notice how it does not matter in which order you evaluate + and * in this expression due to my use of parentheses.
PEMDAS is notation. It has no influence on the actual underlying math, only how we write it.
You're absolutely right, not sure what I was thinking.
Thanks, I've been trying to figure out how to put this and you did it concisely!