Parenthesis/Exponents-Multiplication/Division-Addition/Subtraction
What/where is the theorem for this and where is the proof?
How do we know it is true?
Descartes’ is arguably when of the greatest genuis’ of all time but just because he says so does it make it so?
Did he say “I think it therefore it is?”
I wanna know!
I assume you’re talking about the order of operations for evaluating arithmetic expressions. In this case, there is no theorem; it’s simply a convention we’ve agreed upon so that expressions like 4*3^2+12 are unambiguous.
Thats not good enough darn it.
I WANT PROOF!
Then I can’t help you. There is no proof. Nowhere. No way. No how.
It really is just a convention. There’s no reason why you can’t define a different ordering. In fact, so long as you tell people what it is and when you’re using it, you could even use it in everyday life.
I’m going to take that back. The reason we use that order of operations is because it gives the right answer. For instance, if I make two three-by-three squares of eggs and throw four more on top, the correct number of eggs (22) is given by the PEMDAS order of operations. While I can’t prove that this order of operations is correct, I can tell you that any other ordering would give the wrong answer to this problem, given the standard interpretation of the English description. Is that better?
As has been said by ultrafilter, there is no proof for the order of arithmetical operations. That’s like saying you want proof that a chair is really called “chair.” Because it’s not truly called “chair,” that’s just something that english-speaking people have agreed upon so that we’d all know how to refer to the object in such a way that other people understand. Math is a made-up system, and any system needs rules. Since Math is made-up, so are its rules. That’s pretty much all there is to it.
Descartes didn’t say “I think it therefore it is,” I don’t know if you’re asking if that was his original statement or if he also made that statement as an extension of his original, which was: “I think therefore I am.” Cogito ergo sum. It was actually part of a complex line of reasoning, he didn’t just come out of nowhere with it. Just go read his Discourse on Method, it’s very rewarding. And not a difficult read. And it will answer your question as to “just because he says so does it make it so?”
If that were true, Angelina Jolie would be sitting in my lap right now.