So, you’re saying that, some time after 1928, a mathematician proved that a ÷ b × c = (a ÷ b) × c? Where was this result published? What’s the citation? Who was the author (or authors)? Or maybe you don’t have the citation to hand, but know the proof off the top of your head? Please, let me see it.
Does it not seem weird to you that such a basic aspect of mathematics as multiplication and division remained undiscovered until the 20th century? It’s hardly Fermat’s Last Theorem. If the meaning of a ÷ b × c were not a matter of choice but instead an open question, why were mathematicians using the notation at all when its meaning was not known?
And what of the textbooks like High School Algebra, Elementary Course (1917) which used the convention - err oops, rule - of performing multiplication first? See page 212, example 155. (Would be 810, not 90, if using strict left-to-right priority for division and multiplication)
If it were proved that this convention is wrong, then you will surely be able to find some serious error that flows from doing division in this order. After all, from any contradiction, you can prove anything.
Of course you won’t be able to do this because the question that you are saying was proved is “what does the sequence of symbols a ÷ b × c mean”. The meaning of sequences of symbols is not a fundamental aspect of the universe, is it. They could have different meanings to different people, in different places, or at different times, couldn’t they?
So, you’re saying that, some time after 1928, a mathematician proved that a ÷ b × c = (a ÷ b) × c? Where was this result published? What’s the citation? Who was the author (or authors)? Or maybe you don’t have the citation to hand, but know the proof off the top of your head? Please, let me see it.
Does it not seem weird to you that such a basic aspect of mathematics as multiplication and division remained undiscovered until the 20th century? It’s hardly Fermat’s Last Theorem. If the meaning of a ÷ b × c were not a matter of choice but instead an open question, why were mathematicians using the notation at all when its meaning was not known?
And what of the textbooks like High School Algebra, Elementary Course (1917) which used the convention - err oops, rule - of performing multiplication first? See page 212, example 155. (Would be 810, not 90, if using strict left-to-right priority for division and multiplication)
If it were proved that this
conventionis wrong, then you will surely be able to find some serious error that flows from doing division in this order. After all, from any contradiction, you can prove anything.Of course you won’t be able to do this because the question that you are saying was proved is “what does the sequence of symbols a ÷ b × c mean”. The meaning of sequences of symbols is not a fundamental aspect of the universe, is it. They could have different meanings to different people, in different places, or at different times, couldn’t they?