That’s just clutter for no good reason when we can just say if it doesn’t have parentheses it’s left to right. Having a default evaluation order makes sense and means we only need parentheses when we want to deviate from the norm.
You’re literally arguing nothing right now. THEY took the position we should have brackets defining the order in every single equation or otherwise have them as undefined TODAY. It doesn’t matter when they were invented. Obviously it’s never been written like that. They are the one arguing it SHOULD BE. I said that would be stupid vs following the left to right convention already established. You’re getting caught up in the semantics of the wording.
What you inferred: they’re saying brackets were always around and we chose left to right to avoid bracket mess.
What I was actually saying: we chose and continue to choose to keep using the left to right convention over brackets everywhere because it would be unnecessary and make things more cluttered.
And yes, that IS a position mathematicians COULD have chosen once brackets WERE invented. They could have decided we should use them in every equation for absolute clarity of order. Saying we should not do that based on tradition alone is a bad reason.
The “always been the case” argument could justify any legacy system. We don’t still use Roman numerals for arithmetic just because they were traditional. Things DO change.
Ancient Greeks and Romans strongly resisted zero as a concept, viewing it as philosophically problematic. Negative numbers were even more controversial with many mathematicians into the Renaissance calling them “fictitious” or “absurd numbers.” It took centuries for these to become accepted as legitimate mathematical objects.
Before Robert Recorde introduced “=” in 1557, mathematicians wrote out “is equal to” in words. Even after its introduction, many resisted it for decades, preferring verbal descriptions or other symbols.
I could go on but if you’re going to argue why something shouldn’t be the case, you should argue more than “it’s tradition” or “we’ve done fine without it so far”. Because they did fine with many things in mathematics until they decided they needed to change or expand it.
THEY took the position we should have brackets defining the order in every single equation or otherwise have them as undefined TODAY
Who’s this mysterious “THEY” you are referring to, because I can assure you that the history of Maths tells you that is wrong. e.g. look in Cajori and you’ll find the order of operations rules are at least 2 centuries older than the use of Brackets in Maths.,
It doesn’t matter when they were invented
The rules haven’t changed since then.
They are the one arguing it SHOULD BE
…and watch Physicists and Mathematicians promptly run out of room on blackboards if they did.
You’re getting caught up in the semantics of the wording
No, you’re making up things that never happened.
they’re saying brackets were always around and we chose left to right to avoid bracket mess
and that’s wrong. Left to right was around before Brackets were.
we chose and continue to choose to keep using the left to right convention over brackets everywhere
and you’re wrong, because that choice was made before we’d even started using Brackets in Maths, by at least a couple of centuries.
it would be unnecessary and make things more cluttered
They’ve always been un-necessary, unless you want to deviate from the normal order of operations.
They could have decided we should use them in every equation for absolute clarity of order
But they didn’t, because we already had clarity over order, and had done for several centuries.
Saying we should not do that based on tradition alone is a bad reason.
Got nothing to do with tradition. Got no idea where you got that idea from.
Things DO change.
The order of operations rules don’t, and the last change to the notation was in the 19th Century.
I could go on
and you’d still be wrong. You’re heading off into completely unrelated topics now.
you should argue more than “it’s tradition” or “we’ve done fine without it so far”
I never said either of those things.
Because they did fine with many things in mathematics until they decided they needed to change or expand it
And they changed the meaning of the Division symbol sometime in the 19th Century or earlier, and everything has been settled for centuries now.
It’s so we don’t have to spam brackets everywhere
9+2-1+6-4+7-3+5=
Becomes
((((((9+2)-1)+6)-4)+7)-3)+5=
That’s just clutter for no good reason when we can just say if it doesn’t have parentheses it’s left to right. Having a default evaluation order makes sense and means we only need parentheses when we want to deviate from the norm.
No it isn’t. The order of operations rules were around for several centuries before we even started using Brackets in Maths.
It was literally never written like that
That has always been the case
You’re literally arguing nothing right now. THEY took the position we should have brackets defining the order in every single equation or otherwise have them as undefined TODAY. It doesn’t matter when they were invented. Obviously it’s never been written like that. They are the one arguing it SHOULD BE. I said that would be stupid vs following the left to right convention already established. You’re getting caught up in the semantics of the wording.
What you inferred: they’re saying brackets were always around and we chose left to right to avoid bracket mess.
What I was actually saying: we chose and continue to choose to keep using the left to right convention over brackets everywhere because it would be unnecessary and make things more cluttered.
And yes, that IS a position mathematicians COULD have chosen once brackets WERE invented. They could have decided we should use them in every equation for absolute clarity of order. Saying we should not do that based on tradition alone is a bad reason.
The “always been the case” argument could justify any legacy system. We don’t still use Roman numerals for arithmetic just because they were traditional. Things DO change.
Ancient Greeks and Romans strongly resisted zero as a concept, viewing it as philosophically problematic. Negative numbers were even more controversial with many mathematicians into the Renaissance calling them “fictitious” or “absurd numbers.” It took centuries for these to become accepted as legitimate mathematical objects.
Before Robert Recorde introduced “=” in 1557, mathematicians wrote out “is equal to” in words. Even after its introduction, many resisted it for decades, preferring verbal descriptions or other symbols.
I could go on but if you’re going to argue why something shouldn’t be the case, you should argue more than “it’s tradition” or “we’ve done fine without it so far”. Because they did fine with many things in mathematics until they decided they needed to change or expand it.
Who’s this mysterious “THEY” you are referring to, because I can assure you that the history of Maths tells you that is wrong. e.g. look in Cajori and you’ll find the order of operations rules are at least 2 centuries older than the use of Brackets in Maths.,
The rules haven’t changed since then.
…and watch Physicists and Mathematicians promptly run out of room on blackboards if they did.
No, you’re making up things that never happened.
and that’s wrong. Left to right was around before Brackets were.
and you’re wrong, because that choice was made before we’d even started using Brackets in Maths, by at least a couple of centuries.
They’ve always been un-necessary, unless you want to deviate from the normal order of operations.
But they didn’t, because we already had clarity over order, and had done for several centuries.
Got nothing to do with tradition. Got no idea where you got that idea from.
The order of operations rules don’t, and the last change to the notation was in the 19th Century.
and you’d still be wrong. You’re heading off into completely unrelated topics now.
I never said either of those things.
And they changed the meaning of the Division symbol sometime in the 19th Century or earlier, and everything has been settled for centuries now.
The “mysterious” they is HerelAm, the person I was replying to you ninny.