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Jtrain360 t1_jacxfwx wrote

Reply to comment by StupidLemonEater in ELI5 How did we figure out the order for PEMDAS? Like how do we know that that order is correct? by ToodlyGoodness

Say you were calculating the trajectory of a probe on its way to one of Jupiter's moons (Europa Clipper for a real world example). Your plan is to launch from Earth, and with the help of both Earth and Mars' gravity three years later to launch the probe into Jupiter's orbit.

The calculations for this would be complex and orders of operations would absolutely matter. Would these calculations even be possible using a different order of operations? I know if we did, our equations would have to be different, I just can't begin to imagine what that would look like.

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Emyrssentry t1_jad1axu wrote

All you really need is a system for denoting "do this part before you calculate the rest" (parentheses). As long as you have that, you can do every calculation exactly right, regardless of whatever other order of operations you have.

The only issue you'd have is clarity. A dozen nested parentheses is not a recipe for clear equations.

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hirmuolio t1_jadcp9h wrote

We can write math without any "order of operations". It is just inner functions (or rather relations) all the way down.

It gets really ugly looking really fast. So you never do it unless you have to prove something involving order of operations.

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