▲ 690 ▼ Math is not a democracy (lemmy.world) submitted 8 months ago by Mog_Spawn@lemmy.world to c/memes@lemmy.world 228 comments fedilink hide all child comments
[–] SmartmanApps@programming.dev 1 point 7 months ago (1 child) answer the question, deflecter :) I haven't deflected. I told you to go read up on the history of it and you would discover what was being talked about. Since you apparently don't know how to use Google either, here's a link for you permalink fedilink source parent hideshow 2 child comments replies: [–] FishFace@piefed.social 0 points 7 months ago (1 child) The contents of the book day nothing about the "rules" only about the symbols, so lining this book doesn't answer the question. In general, responding to a question with "you haven't read enough" is, indeed, deflection, and is a sign you can't answer. If you could, you would! Simple. permalink fedilink source parent hideshow 2 child comments replies: [–] SmartmanApps@programming.dev 1 point 7 months ago (1 child) The contents of the book day nothing about the “rules” only about the symbols says person proving they didn't read it. Who woulda thought you might refuse to read something that would prove you wrong. 🙄 In general, responding to a question with “you haven’t read enough” is, indeed, deflection says person revealing they don't know what deflection means either 🙄 a sign you can’t answer I can answer if you go ahead and book some online tutoring with me to cover the history behind the comment. If you could, you would! Simple It's not my job to educate you dude, unless you book some online tutoring with me, in which case it is my job. I gave you a book which answers it, for free, in extreme detail, and you lied about what it even contains, cos you never even looked at it, simple. permalink fedilink source parent hideshow 2 child comments replies: [–] FishFace@piefed.social 0 points 7 months ago (1 child) Hey, you're right, Cajori does talk about operator precedence. Unfortunately, it talks about how the rules, especially for mixed division and multiplication, have changed over time. Supporting my point that these "rules" are not in fact rules of maths, but instead rules of mathematicians. That is why Cajori includes them in a book about the history of how we write mathematics. No matter how you write multiplication and addition, they must always be commutative, associative relations which obey the distributive law; if they didn't, they wouldn't be multiplication and addition. However, you can write them down in different ways, by using different symbols for example. Using different symbols for multiplication changes what a sequence of mathematical symbols means, but it doesn't change what multiplication is. Doing the operations described by a sequence of mathematical symbols in one order or another order may break one set of rules of precedence, but those are rules made by mathematicians not by the fundamental working of the universe. How do I know this? Because Cajori says that, at the time he was writing, there was "no agreement" over the order in which to perform divisions and multiplications if both occur in an expression. So here's a question for you: do you agree with Cajori that at one time there was no agreement over which order to perform multiplications and divisions, or not? If you do agree that there was no such agreement, do you then agree that, for there to be agreement now, such as there may be, that change must be through rules created by mathematicians, rather than by rules given to us from the universe itself? Because the universe certainly didn't change in the meantime, did it? If you don't agree then that would rather expose your fetishisation of textbooks as hollow trolling, of course. permalink fedilink source parent hideshow 2 child comments replies: [–] SmartmanApps@programming.dev 1 point 7 months ago (1 child) especially for mixed division and multiplication, have changed over time and yet, have not changed since he died. 😂 Keep going - you're on the right track but the rabbit hole is deeper Supporting my point that these “rules” are not in fact rules of maths says person who doesn't know the difference between rules and conventions, and thus does not support what you are saying 😂 instead rules of mathematicians who proved them, yes associative relations which obey the distributive law Property, not Law, yes may break one set of rules of precedence there's only one set! 😂 those are rules made by mathematicians not by the fundamental working of the universe says person failing to give a single example of such 😂 How do I know this? Same way you "know" everything - you just make it up as you go along, but never can produce any evidence to support you 😂 at the time he was writing, there was “no agreement” over the order in which to perform divisions and multiplications if both occur in an expression Yep, and why was that, or have you already forgotten the assignment? 😂 So here’s a question for you: do you agree with Cajori that at one time there was no agreement over which order to perform multiplications and divisions, or not? Of course, and I, unlike you, know exactly what he was talking about 😂 do you then agree that, for there to be agreement now There isn't, given he was talking about conventions, and now, same as then, different people use different conventions, but all of them obey the rules 🙄 that change must be through rules created by mathematicians from proof of same rules given to us from the universe itself? NOW you're getting it! Because the universe certainly didn’t change in the meantime, did it? Nope, and neither have the rules 😂 If you don’t agree then that would rather expose your fetishisation of textbooks as hollow trolling, of course. And, yet I did agree, sorry to spoil your fun. 🤣🤣🤣 BTW Cajori isn't a textbook, in case you didn't notice 😂 permalink fedilink source parent hideshow 2 child comments replies: [–] FishFace@piefed.social 1 point 7 months ago* (last edited 6 months ago) Property, not Law, yes an old textbook (p78. Note, before quibbling about "products", that even though it is expressed by juxtaposition, on page 1 this textbook says that, "multiplication is indicated by the absence of a sign" and we are in the multiplication, not the non-existent "product" section. The following exercises are explicitly multiplication.) a new textbook (p31) (Note that this time the law is expressed with × symbols. I also note that this textbook is the exact same publisher - CGP - that you have screenshotted in support of your own claims elsewhere, and indeed we used CGP textbooks at school.) and a teacher resource (p5) (published by the University of Melbourne for teaching primary and secondary students) All call it the "distributive law". The second textbook uses the term interchangeably with "distributive property" (p34). A five-second google can find numerous webpages, with an introductory paragraph which starts, "the distributive law, also called the distributive property..." and Encylopedia Britannica says too that they are the same thing. All three resources make no distinction as far as distribution goes between an expression written with a multiplication symbol like 2×(4+5) and one without like 2(x+3). There is no difference between the two terms. I'd ask you for your reference, but I'm sure it's in the same place as your references to your other nonsense that you tried and failed to find references for, so you needn't bother: the evidence above is all that's needed to dismiss this bollocks anyway. So stop repeating this stupid claim; nobody except a complete moron is going to use these two terms - which certainly sound like synonyms - to refer to two closely related, but different things. It's asking for confusion. I don't intend to discuss this point again. who proved them, yes from proof of same 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? permalink fedilink source parent
[–] FishFace@piefed.social 0 points 7 months ago (1 child) The contents of the book day nothing about the "rules" only about the symbols, so lining this book doesn't answer the question. In general, responding to a question with "you haven't read enough" is, indeed, deflection, and is a sign you can't answer. If you could, you would! Simple. permalink fedilink source parent hideshow 2 child comments replies: [–] SmartmanApps@programming.dev 1 point 7 months ago (1 child) The contents of the book day nothing about the “rules” only about the symbols says person proving they didn't read it. Who woulda thought you might refuse to read something that would prove you wrong. 🙄 In general, responding to a question with “you haven’t read enough” is, indeed, deflection says person revealing they don't know what deflection means either 🙄 a sign you can’t answer I can answer if you go ahead and book some online tutoring with me to cover the history behind the comment. If you could, you would! Simple It's not my job to educate you dude, unless you book some online tutoring with me, in which case it is my job. I gave you a book which answers it, for free, in extreme detail, and you lied about what it even contains, cos you never even looked at it, simple. permalink fedilink source parent hideshow 2 child comments replies: [–] FishFace@piefed.social 0 points 7 months ago (1 child) Hey, you're right, Cajori does talk about operator precedence. Unfortunately, it talks about how the rules, especially for mixed division and multiplication, have changed over time. Supporting my point that these "rules" are not in fact rules of maths, but instead rules of mathematicians. That is why Cajori includes them in a book about the history of how we write mathematics. No matter how you write multiplication and addition, they must always be commutative, associative relations which obey the distributive law; if they didn't, they wouldn't be multiplication and addition. However, you can write them down in different ways, by using different symbols for example. Using different symbols for multiplication changes what a sequence of mathematical symbols means, but it doesn't change what multiplication is. Doing the operations described by a sequence of mathematical symbols in one order or another order may break one set of rules of precedence, but those are rules made by mathematicians not by the fundamental working of the universe. How do I know this? Because Cajori says that, at the time he was writing, there was "no agreement" over the order in which to perform divisions and multiplications if both occur in an expression. So here's a question for you: do you agree with Cajori that at one time there was no agreement over which order to perform multiplications and divisions, or not? If you do agree that there was no such agreement, do you then agree that, for there to be agreement now, such as there may be, that change must be through rules created by mathematicians, rather than by rules given to us from the universe itself? Because the universe certainly didn't change in the meantime, did it? If you don't agree then that would rather expose your fetishisation of textbooks as hollow trolling, of course. permalink fedilink source parent hideshow 2 child comments replies: [–] SmartmanApps@programming.dev 1 point 7 months ago (1 child) especially for mixed division and multiplication, have changed over time and yet, have not changed since he died. 😂 Keep going - you're on the right track but the rabbit hole is deeper Supporting my point that these “rules” are not in fact rules of maths says person who doesn't know the difference between rules and conventions, and thus does not support what you are saying 😂 instead rules of mathematicians who proved them, yes associative relations which obey the distributive law Property, not Law, yes may break one set of rules of precedence there's only one set! 😂 those are rules made by mathematicians not by the fundamental working of the universe says person failing to give a single example of such 😂 How do I know this? Same way you "know" everything - you just make it up as you go along, but never can produce any evidence to support you 😂 at the time he was writing, there was “no agreement” over the order in which to perform divisions and multiplications if both occur in an expression Yep, and why was that, or have you already forgotten the assignment? 😂 So here’s a question for you: do you agree with Cajori that at one time there was no agreement over which order to perform multiplications and divisions, or not? Of course, and I, unlike you, know exactly what he was talking about 😂 do you then agree that, for there to be agreement now There isn't, given he was talking about conventions, and now, same as then, different people use different conventions, but all of them obey the rules 🙄 that change must be through rules created by mathematicians from proof of same rules given to us from the universe itself? NOW you're getting it! Because the universe certainly didn’t change in the meantime, did it? Nope, and neither have the rules 😂 If you don’t agree then that would rather expose your fetishisation of textbooks as hollow trolling, of course. And, yet I did agree, sorry to spoil your fun. 🤣🤣🤣 BTW Cajori isn't a textbook, in case you didn't notice 😂 permalink fedilink source parent hideshow 2 child comments replies: [–] FishFace@piefed.social 1 point 7 months ago* (last edited 6 months ago) Property, not Law, yes an old textbook (p78. Note, before quibbling about "products", that even though it is expressed by juxtaposition, on page 1 this textbook says that, "multiplication is indicated by the absence of a sign" and we are in the multiplication, not the non-existent "product" section. The following exercises are explicitly multiplication.) a new textbook (p31) (Note that this time the law is expressed with × symbols. I also note that this textbook is the exact same publisher - CGP - that you have screenshotted in support of your own claims elsewhere, and indeed we used CGP textbooks at school.) and a teacher resource (p5) (published by the University of Melbourne for teaching primary and secondary students) All call it the "distributive law". The second textbook uses the term interchangeably with "distributive property" (p34). A five-second google can find numerous webpages, with an introductory paragraph which starts, "the distributive law, also called the distributive property..." and Encylopedia Britannica says too that they are the same thing. All three resources make no distinction as far as distribution goes between an expression written with a multiplication symbol like 2×(4+5) and one without like 2(x+3). There is no difference between the two terms. I'd ask you for your reference, but I'm sure it's in the same place as your references to your other nonsense that you tried and failed to find references for, so you needn't bother: the evidence above is all that's needed to dismiss this bollocks anyway. So stop repeating this stupid claim; nobody except a complete moron is going to use these two terms - which certainly sound like synonyms - to refer to two closely related, but different things. It's asking for confusion. I don't intend to discuss this point again. who proved them, yes from proof of same 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? permalink fedilink source parent
[–] SmartmanApps@programming.dev 1 point 7 months ago (1 child) The contents of the book day nothing about the “rules” only about the symbols says person proving they didn't read it. Who woulda thought you might refuse to read something that would prove you wrong. 🙄 In general, responding to a question with “you haven’t read enough” is, indeed, deflection says person revealing they don't know what deflection means either 🙄 a sign you can’t answer I can answer if you go ahead and book some online tutoring with me to cover the history behind the comment. If you could, you would! Simple It's not my job to educate you dude, unless you book some online tutoring with me, in which case it is my job. I gave you a book which answers it, for free, in extreme detail, and you lied about what it even contains, cos you never even looked at it, simple. permalink fedilink source parent hideshow 2 child comments replies: [–] FishFace@piefed.social 0 points 7 months ago (1 child) Hey, you're right, Cajori does talk about operator precedence. Unfortunately, it talks about how the rules, especially for mixed division and multiplication, have changed over time. Supporting my point that these "rules" are not in fact rules of maths, but instead rules of mathematicians. That is why Cajori includes them in a book about the history of how we write mathematics. No matter how you write multiplication and addition, they must always be commutative, associative relations which obey the distributive law; if they didn't, they wouldn't be multiplication and addition. However, you can write them down in different ways, by using different symbols for example. Using different symbols for multiplication changes what a sequence of mathematical symbols means, but it doesn't change what multiplication is. Doing the operations described by a sequence of mathematical symbols in one order or another order may break one set of rules of precedence, but those are rules made by mathematicians not by the fundamental working of the universe. How do I know this? Because Cajori says that, at the time he was writing, there was "no agreement" over the order in which to perform divisions and multiplications if both occur in an expression. So here's a question for you: do you agree with Cajori that at one time there was no agreement over which order to perform multiplications and divisions, or not? If you do agree that there was no such agreement, do you then agree that, for there to be agreement now, such as there may be, that change must be through rules created by mathematicians, rather than by rules given to us from the universe itself? Because the universe certainly didn't change in the meantime, did it? If you don't agree then that would rather expose your fetishisation of textbooks as hollow trolling, of course. permalink fedilink source parent hideshow 2 child comments replies: [–] SmartmanApps@programming.dev 1 point 7 months ago (1 child) especially for mixed division and multiplication, have changed over time and yet, have not changed since he died. 😂 Keep going - you're on the right track but the rabbit hole is deeper Supporting my point that these “rules” are not in fact rules of maths says person who doesn't know the difference between rules and conventions, and thus does not support what you are saying 😂 instead rules of mathematicians who proved them, yes associative relations which obey the distributive law Property, not Law, yes may break one set of rules of precedence there's only one set! 😂 those are rules made by mathematicians not by the fundamental working of the universe says person failing to give a single example of such 😂 How do I know this? Same way you "know" everything - you just make it up as you go along, but never can produce any evidence to support you 😂 at the time he was writing, there was “no agreement” over the order in which to perform divisions and multiplications if both occur in an expression Yep, and why was that, or have you already forgotten the assignment? 😂 So here’s a question for you: do you agree with Cajori that at one time there was no agreement over which order to perform multiplications and divisions, or not? Of course, and I, unlike you, know exactly what he was talking about 😂 do you then agree that, for there to be agreement now There isn't, given he was talking about conventions, and now, same as then, different people use different conventions, but all of them obey the rules 🙄 that change must be through rules created by mathematicians from proof of same rules given to us from the universe itself? NOW you're getting it! Because the universe certainly didn’t change in the meantime, did it? Nope, and neither have the rules 😂 If you don’t agree then that would rather expose your fetishisation of textbooks as hollow trolling, of course. And, yet I did agree, sorry to spoil your fun. 🤣🤣🤣 BTW Cajori isn't a textbook, in case you didn't notice 😂 permalink fedilink source parent hideshow 2 child comments replies: [–] FishFace@piefed.social 1 point 7 months ago* (last edited 6 months ago) Property, not Law, yes an old textbook (p78. Note, before quibbling about "products", that even though it is expressed by juxtaposition, on page 1 this textbook says that, "multiplication is indicated by the absence of a sign" and we are in the multiplication, not the non-existent "product" section. The following exercises are explicitly multiplication.) a new textbook (p31) (Note that this time the law is expressed with × symbols. I also note that this textbook is the exact same publisher - CGP - that you have screenshotted in support of your own claims elsewhere, and indeed we used CGP textbooks at school.) and a teacher resource (p5) (published by the University of Melbourne for teaching primary and secondary students) All call it the "distributive law". The second textbook uses the term interchangeably with "distributive property" (p34). A five-second google can find numerous webpages, with an introductory paragraph which starts, "the distributive law, also called the distributive property..." and Encylopedia Britannica says too that they are the same thing. All three resources make no distinction as far as distribution goes between an expression written with a multiplication symbol like 2×(4+5) and one without like 2(x+3). There is no difference between the two terms. I'd ask you for your reference, but I'm sure it's in the same place as your references to your other nonsense that you tried and failed to find references for, so you needn't bother: the evidence above is all that's needed to dismiss this bollocks anyway. So stop repeating this stupid claim; nobody except a complete moron is going to use these two terms - which certainly sound like synonyms - to refer to two closely related, but different things. It's asking for confusion. I don't intend to discuss this point again. who proved them, yes from proof of same 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? permalink fedilink source parent
[–] FishFace@piefed.social 0 points 7 months ago (1 child) Hey, you're right, Cajori does talk about operator precedence. Unfortunately, it talks about how the rules, especially for mixed division and multiplication, have changed over time. Supporting my point that these "rules" are not in fact rules of maths, but instead rules of mathematicians. That is why Cajori includes them in a book about the history of how we write mathematics. No matter how you write multiplication and addition, they must always be commutative, associative relations which obey the distributive law; if they didn't, they wouldn't be multiplication and addition. However, you can write them down in different ways, by using different symbols for example. Using different symbols for multiplication changes what a sequence of mathematical symbols means, but it doesn't change what multiplication is. Doing the operations described by a sequence of mathematical symbols in one order or another order may break one set of rules of precedence, but those are rules made by mathematicians not by the fundamental working of the universe. How do I know this? Because Cajori says that, at the time he was writing, there was "no agreement" over the order in which to perform divisions and multiplications if both occur in an expression. So here's a question for you: do you agree with Cajori that at one time there was no agreement over which order to perform multiplications and divisions, or not? If you do agree that there was no such agreement, do you then agree that, for there to be agreement now, such as there may be, that change must be through rules created by mathematicians, rather than by rules given to us from the universe itself? Because the universe certainly didn't change in the meantime, did it? If you don't agree then that would rather expose your fetishisation of textbooks as hollow trolling, of course. permalink fedilink source parent hideshow 2 child comments replies: [–] SmartmanApps@programming.dev 1 point 7 months ago (1 child) especially for mixed division and multiplication, have changed over time and yet, have not changed since he died. 😂 Keep going - you're on the right track but the rabbit hole is deeper Supporting my point that these “rules” are not in fact rules of maths says person who doesn't know the difference between rules and conventions, and thus does not support what you are saying 😂 instead rules of mathematicians who proved them, yes associative relations which obey the distributive law Property, not Law, yes may break one set of rules of precedence there's only one set! 😂 those are rules made by mathematicians not by the fundamental working of the universe says person failing to give a single example of such 😂 How do I know this? Same way you "know" everything - you just make it up as you go along, but never can produce any evidence to support you 😂 at the time he was writing, there was “no agreement” over the order in which to perform divisions and multiplications if both occur in an expression Yep, and why was that, or have you already forgotten the assignment? 😂 So here’s a question for you: do you agree with Cajori that at one time there was no agreement over which order to perform multiplications and divisions, or not? Of course, and I, unlike you, know exactly what he was talking about 😂 do you then agree that, for there to be agreement now There isn't, given he was talking about conventions, and now, same as then, different people use different conventions, but all of them obey the rules 🙄 that change must be through rules created by mathematicians from proof of same rules given to us from the universe itself? NOW you're getting it! Because the universe certainly didn’t change in the meantime, did it? Nope, and neither have the rules 😂 If you don’t agree then that would rather expose your fetishisation of textbooks as hollow trolling, of course. And, yet I did agree, sorry to spoil your fun. 🤣🤣🤣 BTW Cajori isn't a textbook, in case you didn't notice 😂 permalink fedilink source parent hideshow 2 child comments replies: [–] FishFace@piefed.social 1 point 7 months ago* (last edited 6 months ago) Property, not Law, yes an old textbook (p78. Note, before quibbling about "products", that even though it is expressed by juxtaposition, on page 1 this textbook says that, "multiplication is indicated by the absence of a sign" and we are in the multiplication, not the non-existent "product" section. The following exercises are explicitly multiplication.) a new textbook (p31) (Note that this time the law is expressed with × symbols. I also note that this textbook is the exact same publisher - CGP - that you have screenshotted in support of your own claims elsewhere, and indeed we used CGP textbooks at school.) and a teacher resource (p5) (published by the University of Melbourne for teaching primary and secondary students) All call it the "distributive law". The second textbook uses the term interchangeably with "distributive property" (p34). A five-second google can find numerous webpages, with an introductory paragraph which starts, "the distributive law, also called the distributive property..." and Encylopedia Britannica says too that they are the same thing. All three resources make no distinction as far as distribution goes between an expression written with a multiplication symbol like 2×(4+5) and one without like 2(x+3). There is no difference between the two terms. I'd ask you for your reference, but I'm sure it's in the same place as your references to your other nonsense that you tried and failed to find references for, so you needn't bother: the evidence above is all that's needed to dismiss this bollocks anyway. So stop repeating this stupid claim; nobody except a complete moron is going to use these two terms - which certainly sound like synonyms - to refer to two closely related, but different things. It's asking for confusion. I don't intend to discuss this point again. who proved them, yes from proof of same 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? permalink fedilink source parent
[–] SmartmanApps@programming.dev 1 point 7 months ago (1 child) especially for mixed division and multiplication, have changed over time and yet, have not changed since he died. 😂 Keep going - you're on the right track but the rabbit hole is deeper Supporting my point that these “rules” are not in fact rules of maths says person who doesn't know the difference between rules and conventions, and thus does not support what you are saying 😂 instead rules of mathematicians who proved them, yes associative relations which obey the distributive law Property, not Law, yes may break one set of rules of precedence there's only one set! 😂 those are rules made by mathematicians not by the fundamental working of the universe says person failing to give a single example of such 😂 How do I know this? Same way you "know" everything - you just make it up as you go along, but never can produce any evidence to support you 😂 at the time he was writing, there was “no agreement” over the order in which to perform divisions and multiplications if both occur in an expression Yep, and why was that, or have you already forgotten the assignment? 😂 So here’s a question for you: do you agree with Cajori that at one time there was no agreement over which order to perform multiplications and divisions, or not? Of course, and I, unlike you, know exactly what he was talking about 😂 do you then agree that, for there to be agreement now There isn't, given he was talking about conventions, and now, same as then, different people use different conventions, but all of them obey the rules 🙄 that change must be through rules created by mathematicians from proof of same rules given to us from the universe itself? NOW you're getting it! Because the universe certainly didn’t change in the meantime, did it? Nope, and neither have the rules 😂 If you don’t agree then that would rather expose your fetishisation of textbooks as hollow trolling, of course. And, yet I did agree, sorry to spoil your fun. 🤣🤣🤣 BTW Cajori isn't a textbook, in case you didn't notice 😂 permalink fedilink source parent hideshow 2 child comments replies: [–] FishFace@piefed.social 1 point 7 months ago* (last edited 6 months ago) Property, not Law, yes an old textbook (p78. Note, before quibbling about "products", that even though it is expressed by juxtaposition, on page 1 this textbook says that, "multiplication is indicated by the absence of a sign" and we are in the multiplication, not the non-existent "product" section. The following exercises are explicitly multiplication.) a new textbook (p31) (Note that this time the law is expressed with × symbols. I also note that this textbook is the exact same publisher - CGP - that you have screenshotted in support of your own claims elsewhere, and indeed we used CGP textbooks at school.) and a teacher resource (p5) (published by the University of Melbourne for teaching primary and secondary students) All call it the "distributive law". The second textbook uses the term interchangeably with "distributive property" (p34). A five-second google can find numerous webpages, with an introductory paragraph which starts, "the distributive law, also called the distributive property..." and Encylopedia Britannica says too that they are the same thing. All three resources make no distinction as far as distribution goes between an expression written with a multiplication symbol like 2×(4+5) and one without like 2(x+3). There is no difference between the two terms. I'd ask you for your reference, but I'm sure it's in the same place as your references to your other nonsense that you tried and failed to find references for, so you needn't bother: the evidence above is all that's needed to dismiss this bollocks anyway. So stop repeating this stupid claim; nobody except a complete moron is going to use these two terms - which certainly sound like synonyms - to refer to two closely related, but different things. It's asking for confusion. I don't intend to discuss this point again. who proved them, yes from proof of same 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? permalink fedilink source parent
[–] FishFace@piefed.social 1 point 7 months ago* (last edited 6 months ago) Property, not Law, yes an old textbook (p78. Note, before quibbling about "products", that even though it is expressed by juxtaposition, on page 1 this textbook says that, "multiplication is indicated by the absence of a sign" and we are in the multiplication, not the non-existent "product" section. The following exercises are explicitly multiplication.) a new textbook (p31) (Note that this time the law is expressed with × symbols. I also note that this textbook is the exact same publisher - CGP - that you have screenshotted in support of your own claims elsewhere, and indeed we used CGP textbooks at school.) and a teacher resource (p5) (published by the University of Melbourne for teaching primary and secondary students) All call it the "distributive law". The second textbook uses the term interchangeably with "distributive property" (p34). A five-second google can find numerous webpages, with an introductory paragraph which starts, "the distributive law, also called the distributive property..." and Encylopedia Britannica says too that they are the same thing. All three resources make no distinction as far as distribution goes between an expression written with a multiplication symbol like 2×(4+5) and one without like 2(x+3). There is no difference between the two terms. I'd ask you for your reference, but I'm sure it's in the same place as your references to your other nonsense that you tried and failed to find references for, so you needn't bother: the evidence above is all that's needed to dismiss this bollocks anyway. So stop repeating this stupid claim; nobody except a complete moron is going to use these two terms - which certainly sound like synonyms - to refer to two closely related, but different things. It's asking for confusion. I don't intend to discuss this point again. who proved them, yes from proof of same 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? permalink fedilink source parent
