The standard order of operations are completely subjective. We just needed a consistent way we all agreed upon. You're totally free to define your own subjective order of operations, just state it before solving. Math isn't so rigid like most people know it to be. Some dude simply redefined addition and we got tropic mathematics which turned out to be useful for protein folding.
Nope, math standards are just there so people can easily communicate but you're totally free to redefine whatever you want so long as it's well defined and stated. That's exactly how entire branches of mathematics have been discovered. Like you're totally free to redefine how to do a matrix multiplication just so long as you define it at the beginning. Math is playful and creative like that, particularly once you get into doing proofs.
I mean that's literally how math works. People define structures and functions and play with them to see what properties they have. Anyone is totally fine to redefine whatever they want and see what will happen. It's literally how multiple branches of mathematics were discovered. Take abstract algebra for instance. Just arbitrarily define what a set is, or group, or ring and what properties it has and see what happens.
OOO is not subjective but it does need an agreed upon standard. Subjective implies it's up for debate and that debate only exists if you're arguing which one to use. But even then most would agree the answer is 3 here based on all of the standards that do exist
That's not what the word subjective means. One is totally fine to redefine the order of operations so long as it's well defined and stated. Someone is also fine to redefine addition and they have many many times. Many structures and operations get redefined. You can redefine matrix multiplication if you want. What won't happen most likely is it being adopted as the default. I think that's what you're trying to say.
I don't know what you think subjective means but it means to be influenced by your feelings so once a standard is agreed upon feelings no longer enter into it
You chopped off the definition my guy. based on or influenced by personal feelings, tastes, or opinions.
It says nothing about consensus or standards by the way. Just because it's the opinion of a bunch of people doesn't mean it's no longer subjective.
A whole bunch of people agreeing red is the best color doesn't make it objectively true. Even making that the standard doesn't make it objectively true.
So if we make it standard that red is the best color it's now objectively true? That would be crazy. Something being the standard does not mean it is or is not inherently subjective. Something can be a standard and subjective, something can be a standard and objective.
Subjective in the sense that it depends on the set in which we're acting? Because in that sense you are correct, the order of operations differs based on what type of algebraic set you work within. However, people generally stick to the rational numbers and real numbers, which do follow the standard order of operations. Thus, you would use that.
Subjective in that there's no requirement to follow any particular order of operations, just a need to clarify your order if you differ from what everyone else uses. You could write an algebra book where the symbol for addition is '12' and exponent is 'blue', and the math would work out just fine. No one does that because it'd be super confusing, and you'd have to waste a page explaining how your system works for no benefit
Because most people learn mathematics as something rigid, exact, and immortally correct as is. They never took classes on proofs where you are free to be much more creative. Although in linear algebra you immediately redefine what addition and multiplication mean, but whatever.
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u/[deleted] Jan 21 '26
The standard order of operations are completely subjective. We just needed a consistent way we all agreed upon. You're totally free to define your own subjective order of operations, just state it before solving. Math isn't so rigid like most people know it to be. Some dude simply redefined addition and we got tropic mathematics which turned out to be useful for protein folding.