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OT: Those arithmetic questions

Started by Unknown January 23, 2018
On 06.02.2018 3:26, Tom Gardner wrote:
> On 06/02/18 00:23, Tom Gardner wrote: >> On 05/02/18 23:35, Les Cargill wrote: >>> Tom Gardner wrote: >>>> On 03/02/18 03:43, Les Cargill wrote: >>>>> Tom Gardner wrote: >>>>>> On 02/02/18 22:29, Les Cargill wrote: >>>>>>> Steve Underwood wrote: >>>>>>>> On 02/02/2018 02:07 PM, Tom Gardner wrote: >>>>>>>>> On 02/02/18 10:07, Steve Underwood wrote: >>>>>>>>>> On 01/24/2018 06:48 PM, gyansorova@gmail.com wrote: >>>>>>>>>>> Sure, it's not what we know that I am commenting about >>>>>>>>>>> though, it is how kids at school are taught >>>>>>>>>>> >>>>>>>>>>> read this mathematicians comments >>>>>>>>>>> >>>>>>>>>>> https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>>> >> As in a lot of the discussions on this topic, I see that article refer to >>>>>>>>>> PEMDAS. Its usually described as something pretty old, that all >>>>>>>>>> school kids are taught. Was anyone here taught PEMDAS? I >>>>>>>>>> certainly wasn't. >>>>>>>>> >>>>>>>>> I, and everyone else of my age, was taught BEDMAS, which is the >>>>>>>>> same thing. That's not to say everyone remembered it. Even >>>>>>>>> teachers can and do think 1+2*3 is 9. >>>>>>>> >>>>>>>> I just asked my children, who are 18 and 20. They had never heard >>>>>>>> of PEMDAS or BEDMAS as mnemonics. They do, however, know that 1+2*3 >>>>>>>> is 7. Its just division that makes things woolly. >>>>>>>> >>>>>>>> Steve >>>>>>>> >>>>>>> >>>>>>> 1+2*3 with a classic stack-based Push Down Automata algebraic >>>>>>> calculator will yield 9. So I'd say it is *at best* ambiguous. >>>>>> >>>>>> No, the correct answer to 1+2*3 is not ambiguous. >>>>>> >>>>>> A calculator used as you describe is calculating (1+2)*3, whether or >>>>>> not the operator realises it. >>>>>> >>>>> >>>>> >>>>> You're implying precedence of "*" over "+". Post hoc or argumentum ad >>>>> mind reading. >>>> >>>> I'm not implying anything. I'm merely stating the long established >>>> rules of >>>> maths. >>>> >>>> >>> >>> I just mean that that's what they told us in junior high school to >>> keep from >>> having to answer dumb questions as a convention. >>> >>> I really do mean that "when you read stuff, it depends on the >>> conventions of >>> the people writing the stuff" and that the Junior High School version >>> is not >>> a particularly privileged ... example. >> >> If you really think that, I suggest you have a long >> discussion with some mathematicians. That excludes >> schoolteachers and most engineers. >> >> >>>>> All I am required to do to refute that is provide a single >>>>> counterexample. >>>> >>>> Don't be silly. >>>> >>> >>> Oh, c'mon. There isn't enough silly in the world. :) >>> >>>> "I have a calculator that says 1+2*3 is 0, therefore that's what it >>>> is". >>>> Ahem. >>>> >>> >>> I've had calculators that would offer different answers :) >> >> I have highly intelligent distant relatives[1] that refuse >> to believe that US astronauts walked on the moon. The moon >> landings are all capitalist fake news stories. >> >> [1] as in one has worked with/for Vladimir Putin > > Drat; that escaped too early. > > I intended to note that /clearly/ there is a scientific > debate between people with differing opinions about whether > man landed on the moon or not.
For what it's worth, I haven't ever seen a _scientific_ debate about moon landings. Most of the times that would be engineers/scientists vs. people without a basic grasp of natural sciences. As a more general note, most conspiracy theories are not falsifiable (in Karl Popper's sense), and thus do not qualify as scientific theories. However, authors or proponents of such theories still think that they could do better than admitting that their beloved theory is a matter of faith. To that effect, they invent pseudoscientific arguments which do not hold any scrutiny -- but might sound convincing to a person without a good technical background. And this is the part that really sucks. Strictly speaking, it's impossible to claim that a particular conspiracy theory is wrong -- because ultimately it's a matter of faith (and not of knowledge), and people are free to believe in whatever they want to believe -- but it's possible to claim that the parts of it which constitute a pseudoscientific hoax are patently false. Gene.
Evgeny Filatov wrote:
> On 06.02.2018 3:26, Tom Gardner wrote: >> On 06/02/18 00:23, Tom Gardner wrote: >>> On 05/02/18 23:35, Les Cargill wrote: >>>> Tom Gardner wrote: >>>>> On 03/02/18 03:43, Les Cargill wrote: >>>>>> Tom Gardner wrote: >>>>>>> On 02/02/18 22:29, Les Cargill wrote: >>>>>>>> Steve Underwood wrote: >>>>>>>>> On 02/02/2018 02:07 PM, Tom Gardner wrote: >>>>>>>>>> On 02/02/18 10:07, Steve Underwood wrote: >>>>>>>>>>> On 01/24/2018 06:48 PM, gyansorova@gmail.com wrote: >>>>>>>>>>>> Sure, it's not what we know that I am commenting about >>>>>>>>>>>> though, it is how kids at school are taught >>>>>>>>>>>> >>>>>>>>>>>> read this mathematicians comments >>>>>>>>>>>> >>>>>>>>>>>> https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>>> >>> As in a lot of the discussions on this topic, I see that article >>> refer to >>>>>>>>>>> PEMDAS. Its usually described as something pretty old, that all >>>>>>>>>>> school kids are taught. Was anyone here taught PEMDAS? I >>>>>>>>>>> certainly wasn't. >>>>>>>>>> >>>>>>>>>> I, and everyone else of my age, was taught BEDMAS, which is the >>>>>>>>>> same thing. That's not to say everyone remembered it. Even >>>>>>>>>> teachers can and do think 1+2*3 is 9. >>>>>>>>> >>>>>>>>> I just asked my children, who are 18 and 20. They had never heard >>>>>>>>> of PEMDAS or BEDMAS as mnemonics. They do, however, know that >>>>>>>>> 1+2*3 >>>>>>>>> is 7. Its just division that makes things woolly. >>>>>>>>> >>>>>>>>> Steve >>>>>>>>> >>>>>>>> >>>>>>>> 1+2*3 with a classic stack-based Push Down Automata algebraic >>>>>>>> calculator will yield 9. So I'd say it is *at best* ambiguous. >>>>>>> >>>>>>> No, the correct answer to 1+2*3 is not ambiguous. >>>>>>> >>>>>>> A calculator used as you describe is calculating (1+2)*3, whether or >>>>>>> not the operator realises it. >>>>>>> >>>>>> >>>>>> >>>>>> You're implying precedence of "*" over "+". Post hoc or argumentum ad >>>>>> mind reading. >>>>> >>>>> I'm not implying anything. I'm merely stating the long established >>>>> rules of >>>>> maths. >>>>> >>>>> >>>> >>>> I just mean that that's what they told us in junior high school to >>>> keep from >>>> having to answer dumb questions as a convention. >>>> >>>> I really do mean that "when you read stuff, it depends on the >>>> conventions of >>>> the people writing the stuff" and that the Junior High School version >>>> is not >>>> a particularly privileged ... example. >>> >>> If you really think that, I suggest you have a long >>> discussion with some mathematicians. That excludes >>> schoolteachers and most engineers. >>> >>> >>>>>> All I am required to do to refute that is provide a single >>>>>> counterexample. >>>>> >>>>> Don't be silly. >>>>> >>>> >>>> Oh, c'mon. There isn't enough silly in the world. :) >>>> >>>>> "I have a calculator that says 1+2*3 is 0, therefore that's what it >>>>> is". >>>>> Ahem. >>>>> >>>> >>>> I've had calculators that would offer different answers :) >>> >>> I have highly intelligent distant relatives[1] that refuse >>> to believe that US astronauts walked on the moon. The moon >>> landings are all capitalist fake news stories. >>> >>> [1] as in one has worked with/for Vladimir Putin >> >> Drat; that escaped too early. >> >> I intended to note that /clearly/ there is a scientific >> debate between people with differing opinions about whether >> man landed on the moon or not. > > For what it's worth, I haven't ever seen a _scientific_ debate about > moon landings. Most of the times that would be engineers/scientists vs. > people without a basic grasp of natural sciences. > > As a more general note, most conspiracy theories are not falsifiable (in > Karl Popper's sense), and thus do not qualify as scientific theories. >
Theories which claim there was no moon landing are very clearly conspiracy theories. They're whacko ideas.
> However, authors or proponents of such theories still think that they > could do better than admitting that their beloved theory is a matter of > faith. To that effect, they invent pseudoscientific arguments which do > not hold any scrutiny -- but might sound convincing to a person without > a good technical background. And this is the part that really sucks. > > Strictly speaking, it's impossible to claim that a particular conspiracy > theory is wrong -- because ultimately it's a matter of faith (and not of > knowledge), and people are free to believe in whatever they want to > believe -- but it's possible to claim that the parts of it which > constitute a pseudoscientific hoax are patently false. > > Gene. >
These aren't even pseudoscientific. They are a known artifact of human cognition. Mr. Gardner is either trying to be funny or he's trying to paint my point that operator precedence is fungible as whacko - which is in itself quite funny ( and I'm quite sympathetic to his position ). -- Les Cargill
On 10/02/18 18:40, Les Cargill wrote:
> Evgeny Filatov wrote: >> On 06.02.2018 3:26, Tom Gardner wrote: >>> On 06/02/18 00:23, Tom Gardner wrote: >>>> On 05/02/18 23:35, Les Cargill wrote: >>>>> Tom Gardner wrote: >>>>>> On 03/02/18 03:43, Les Cargill wrote: >>>>>>> Tom Gardner wrote: >>>>>>>> On 02/02/18 22:29, Les Cargill wrote: >>>>>>>>> Steve Underwood wrote: >>>>>>>>>> On 02/02/2018 02:07 PM, Tom Gardner wrote: >>>>>>>>>>> On 02/02/18 10:07, Steve Underwood wrote: >>>>>>>>>>>> On 01/24/2018 06:48 PM, gyansorova@gmail.com wrote: >>>>>>>>>>>>> Sure, it's not what we know that I am commenting >>>>>>>>>>>>> about though, it is how kids at school are taught >>>>>>>>>>>>> >>>>>>>>>>>>> read this mathematicians comments >>>>>>>>>>>>> >>>>>>>>>>>>> https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>>> >>>> >>>>>>>>>>>>>
As in a lot of the discussions on this topic, I see that article refer to
>>>>>>>>>>>> PEMDAS. Its usually described as something pretty old, >>>>>>>>>>>> that all school kids are taught. Was anyone here taught >>>>>>>>>>>> PEMDAS? I certainly wasn't. >>>>>>>>>>> >>>>>>>>>>> I, and everyone else of my age, was taught BEDMAS, which >>>>>>>>>>> is the same thing. That's not to say everyone remembered >>>>>>>>>>> it. Even teachers can and do think 1+2*3 is 9. >>>>>>>>>> >>>>>>>>>> I just asked my children, who are 18 and 20. They had never >>>>>>>>>> heard of PEMDAS or BEDMAS as mnemonics. They do, however, >>>>>>>>>> know that 1+2*3 is 7. Its just division that makes things >>>>>>>>>> woolly. >>>>>>>>>> >>>>>>>>>> Steve >>>>>>>>>> >>>>>>>>> >>>>>>>>> 1+2*3 with a classic stack-based Push Down Automata >>>>>>>>> algebraic calculator will yield 9. So I'd say it is *at best* >>>>>>>>> ambiguous. >>>>>>>> >>>>>>>> No, the correct answer to 1+2*3 is not ambiguous. >>>>>>>> >>>>>>>> A calculator used as you describe is calculating (1+2)*3, >>>>>>>> whether or not the operator realises it. >>>>>>>> >>>>>>> >>>>>>> >>>>>>> You're implying precedence of "*" over "+". Post hoc or >>>>>>> argumentum ad mind reading. >>>>>> >>>>>> I'm not implying anything. I'm merely stating the long established >>>>>> rules of maths. >>>>>> >>>>>> >>>>> >>>>> I just mean that that's what they told us in junior high school to >>>>> keep from having to answer dumb questions as a convention. >>>>> >>>>> I really do mean that "when you read stuff, it depends on the >>>>> conventions of the people writing the stuff" and that the Junior High >>>>> School version is not a particularly privileged ... example. >>>> >>>> If you really think that, I suggest you have a long discussion with >>>> some mathematicians. That excludes schoolteachers and most engineers. >>>> >>>> >>>>>>> All I am required to do to refute that is provide a single >>>>>>> counterexample. >>>>>> >>>>>> Don't be silly. >>>>>> >>>>> >>>>> Oh, c'mon. There isn't enough silly in the world. :) >>>>> >>>>>> "I have a calculator that says 1+2*3 is 0, therefore that's what >>>>>> it is". Ahem. >>>>>> >>>>> >>>>> I've had calculators that would offer different answers :) >>>> >>>> I have highly intelligent distant relatives[1] that refuse to believe >>>> that US astronauts walked on the moon. The moon landings are all >>>> capitalist fake news stories. >>>> >>>> [1] as in one has worked with/for Vladimir Putin >>> >>> Drat; that escaped too early. >>> >>> I intended to note that /clearly/ there is a scientific debate between >>> people with differing opinions about whether man landed on the moon or >>> not. >> >> For what it's worth, I haven't ever seen a _scientific_ debate about moon >> landings. Most of the times that would be engineers/scientists vs. people >> without a basic grasp of natural sciences. >> >> As a more general note, most conspiracy theories are not falsifiable (in >> Karl Popper's sense), and thus do not qualify as scientific theories. >> > > Theories which claim there was no moon landing are very clearly conspiracy > theories. They're whacko ideas.
No! The concept/opinion that man landed on the moon is the conspiracy :) After all, aren't all viewpoints and opinions equally valid?
>> However, authors or proponents of such theories still think that they could >> do better than admitting that their beloved theory is a matter of faith. To >> that effect, they invent pseudoscientific arguments which do not hold any >> scrutiny -- but might sound convincing to a person without a good technical >> background. And this is the part that really sucks. >> >> Strictly speaking, it's impossible to claim that a particular conspiracy >> theory is wrong -- because ultimately it's a matter of faith (and not of >> knowledge), and people are free to believe in whatever they want to believe >> -- but it's possible to claim that the parts of it which constitute a >> pseudoscientific hoax are patently false. >> >> Gene. >> > > These aren't even pseudoscientific. They are a known artifact of human > cognition. Mr. Gardner is either trying to be funny or he's trying to paint > my point that operator precedence is fungible as whacko - which is in itself > quite funny ( and I'm quite sympathetic to his position ).
That's basically it; I was trying to use humour and an absurd (but widely held and believed) belief to highlight the reasoning involved. I can quite understand that someone for whom English is a second language would not have realised that. My apologies. Mind you, too many native English speakers wouldn't have understood that either, due to lack of education and/or being "divided by a common language" :( Fundamentally people are free to - and some do - invent languages with differing rules; APL springs to mind w.r.t. "interesting" results. That's perfectly OK /provided/ that everybody in the conversation understands the non-standard rules. What's /not/ OK is to mutate the rules (usually through ignorance) and then claim that the mutated rules are the right and the original rules are wrong. That would be no better than loudly insisting that non-gender specific pronoun "hir" should replace "his" and "her", on the presumption that English doesn't already have a suitable word such as "their". Yup; I remember people proudly proclaiming that!
Tom Gardner wrote:
> On 10/02/18 18:40, Les Cargill wrote: >> Evgeny Filatov wrote: >>> On 06.02.2018 3:26, Tom Gardner wrote: >>>> On 06/02/18 00:23, Tom Gardner wrote: >>>>> On 05/02/18 23:35, Les Cargill wrote: >>>>>> Tom Gardner wrote: >>>>>>> On 03/02/18 03:43, Les Cargill wrote: >>>>>>>> Tom Gardner wrote: >>>>>>>>> On 02/02/18 22:29, Les Cargill wrote: >>>>>>>>>> Steve Underwood wrote: >>>>>>>>>>> On 02/02/2018 02:07 PM, Tom Gardner wrote: >>>>>>>>>>>> On 02/02/18 10:07, Steve Underwood wrote: >>>>>>>>>>>>> On 01/24/2018 06:48 PM, gyansorova@gmail.com wrote: >>>>>>>>>>>>>> Sure, it's not what we know that I am commenting >>>>>>>>>>>>>> about though, it is how kids at school are taught >>>>>>>>>>>>>> >>>>>>>>>>>>>> read this mathematicians comments >>>>>>>>>>>>>> >>>>>>>>>>>>>> https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>> >>>>>>>>>>>>>> > As in a lot of the discussions on this topic, I see that article refer to >>>>>>>>>>>>> PEMDAS. Its usually described as something pretty old, >>>>>>>>>>>>> that all school kids are taught. Was anyone here taught >>>>>>>>>>>>> PEMDAS? I certainly wasn't. >>>>>>>>>>>> >>>>>>>>>>>> I, and everyone else of my age, was taught BEDMAS, which >>>>>>>>>>>> is the same thing. That's not to say everyone remembered >>>>>>>>>>>> it. Even teachers can and do think 1+2*3 is 9. >>>>>>>>>>> >>>>>>>>>>> I just asked my children, who are 18 and 20. They had never >>>>>>>>>>> heard of PEMDAS or BEDMAS as mnemonics. They do, however, >>>>>>>>>>> know that 1+2*3 is 7. Its just division that makes things >>>>>>>>>>> woolly. >>>>>>>>>>> >>>>>>>>>>> Steve >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> 1+2*3 with a classic stack-based Push Down Automata >>>>>>>>>> algebraic calculator will yield 9. So I'd say it is *at best* >>>>>>>>>> ambiguous. >>>>>>>>> >>>>>>>>> No, the correct answer to 1+2*3 is not ambiguous. >>>>>>>>> >>>>>>>>> A calculator used as you describe is calculating (1+2)*3, >>>>>>>>> whether or not the operator realises it. >>>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> You're implying precedence of "*" over "+". Post hoc or >>>>>>>> argumentum ad mind reading. >>>>>>> >>>>>>> I'm not implying anything. I'm merely stating the long established >>>>>>> rules of maths. >>>>>>> >>>>>>> >>>>>> >>>>>> I just mean that that's what they told us in junior high school to >>>>>> keep from having to answer dumb questions as a convention. >>>>>> >>>>>> I really do mean that "when you read stuff, it depends on the >>>>>> conventions of the people writing the stuff" and that the Junior High >>>>>> School version is not a particularly privileged ... example. >>>>> >>>>> If you really think that, I suggest you have a long discussion with >>>>> some mathematicians. That excludes schoolteachers and most engineers. >>>>> >>>>> >>>>>>>> All I am required to do to refute that is provide a single >>>>>>>> counterexample. >>>>>>> >>>>>>> Don't be silly. >>>>>>> >>>>>> >>>>>> Oh, c'mon. There isn't enough silly in the world. :) >>>>>> >>>>>>> "I have a calculator that says 1+2*3 is 0, therefore that's what >>>>>>> it is". Ahem. >>>>>>> >>>>>> >>>>>> I've had calculators that would offer different answers :) >>>>> >>>>> I have highly intelligent distant relatives[1] that refuse to believe >>>>> that US astronauts walked on the moon. The moon landings are all >>>>> capitalist fake news stories. >>>>> >>>>> [1] as in one has worked with/for Vladimir Putin >>>> >>>> Drat; that escaped too early. >>>> >>>> I intended to note that /clearly/ there is a scientific debate between >>>> people with differing opinions about whether man landed on the moon or >>>> not. >>> >>> For what it's worth, I haven't ever seen a _scientific_ debate about >>> moon >>> landings. Most of the times that would be engineers/scientists vs. >>> people >>> without a basic grasp of natural sciences. >>> >>> As a more general note, most conspiracy theories are not falsifiable (in >>> Karl Popper's sense), and thus do not qualify as scientific theories. >>> >> >> Theories which claim there was no moon landing are very clearly >> conspiracy >> theories. They're whacko ideas. > > No! The concept/opinion that man landed on the moon is the conspiracy :) > > After all, aren't all viewpoints and opinions equally valid? > > > >>> However, authors or proponents of such theories still think that they >>> could >>> do better than admitting that their beloved theory is a matter of >>> faith. To >>> that effect, they invent pseudoscientific arguments which do not hold >>> any >>> scrutiny -- but might sound convincing to a person without a good >>> technical >>> background. And this is the part that really sucks. >>> >>> Strictly speaking, it's impossible to claim that a particular conspiracy >>> theory is wrong -- because ultimately it's a matter of faith (and not of >>> knowledge), and people are free to believe in whatever they want to >>> believe >>> -- but it's possible to claim that the parts of it which constitute a >>> pseudoscientific hoax are patently false. >>> >>> Gene. >>> >> >> These aren't even pseudoscientific. They are a known artifact of human >> cognition. Mr. Gardner is either trying to be funny or he's trying to >> paint >> my point that operator precedence is fungible as whacko - which is in >> itself >> quite funny ( and I'm quite sympathetic to his position ). > > That's basically it; I was trying to use humour and an absurd (but > widely held and believed) belief to highlight the reasoning involved. >
I am very glad that I caught that, then. You have a dry wit.
> I can quite understand that someone for whom English is a second > language would not have realised that. My apologies. Mind you, too many > native English speakers wouldn't have understood that either, due to > lack of education and/or being "divided by a common language" :( > > Fundamentally people are free to - and some do - invent languages with > differing rules; APL springs to mind w.r.t. "interesting" results. > That's perfectly OK /provided/ that everybody in the conversation > understands the non-standard rules. > > What's /not/ OK is to mutate the rules (usually through ignorance) and > then claim that the mutated rules are the right and the original rules > are wrong. >
Oh, I didn't mean that at all. My point continues to be "you gotta know the territory" and the subject makes it easier for my to understand historical phenomena like the Catholic Church getting violent about heresies :)
> That would be no better than loudly insisting that non-gender specific > pronoun "hir" should replace "his" and "her", on the presumption that > English doesn't already have a suitable word such as "their". Yup; I > remember people proudly proclaiming that!
-- Les Cargill
On Tuesday, January 23, 2018 at 12:07:03 PM UTC-8, gyans...@gmail.com wrote:
> Often you see questions on social media such as - find the answer to > > 9/3(1+2) (they usually use the divide symbol which nobody uses of course so I have replaced it with a slash) > > and they spout on about order of operations and so left to right the answer is 3x 3 =9 and the catch is that people answer 9/9 = 1. Ha, they don't know their order of operations which was agreed by convention in 1916 or something. Well is that right? > > Of course when programming in matlab or a computer language we would do > > 9/3*(1+2)=9 and we get 9. If we wanted the other answer we would put > > 9/(3*91+2)) > > To make things confusing though, if you type into a calculator > > 9/3(1+2) it may well give you 1 but if you enter 9/3x(1+2) you get 9. > > > It appears that the calculator engineers are using Juxtaposition and assume that the 3(1+2) is all together whereas adding the x sign reverts to so called Bodmas. > > Now if I showed you this equation > > x=1/ab where a=1 and b=2 you may well say the answer is 0.5 > because you assume the ab is together. > Whereas under the order of operations you get 1x 2 = 2.
I started learning Fortran just before I started Algebra in school. At some point, I found most of the rules similar enough, and didn't have any problem with them. However, in textbook notation, if you put some expression, a horizontal bar, and another expression below, the upper and lower expressions are evaluated before the division (bar). There is no horizontal bar divide operator in Fortran, so this problem never comes up.
On Tuesday, July 24, 2018 at 7:37:16 AM UTC+12, gah...@gmail.com wrote:
> On Tuesday, January 23, 2018 at 12:07:03 PM UTC-8, gyans...@gmail.com wrote: > > Often you see questions on social media such as - find the answer to > > > > 9/3(1+2) (they usually use the divide symbol which nobody uses of course so I have replaced it with a slash) > > > > and they spout on about order of operations and so left to right the answer is 3x 3 =9 and the catch is that people answer 9/9 = 1. Ha, they don't know their order of operations which was agreed by convention in 1916 or something. Well is that right? > > > > Of course when programming in matlab or a computer language we would do > > > > 9/3*(1+2)=9 and we get 9. If we wanted the other answer we would put > > > > 9/(3*91+2)) > > > > To make things confusing though, if you type into a calculator > > > > 9/3(1+2) it may well give you 1 but if you enter 9/3x(1+2) you get 9. > > > > > > It appears that the calculator engineers are using Juxtaposition and assume that the 3(1+2) is all together whereas adding the x sign reverts to so called Bodmas. > > > > Now if I showed you this equation > > > > x=1/ab where a=1 and b=2 you may well say the answer is 0.5 > > because you assume the ab is together. > > Whereas under the order of operations you get 1x 2 = 2. > > I started learning Fortran just before I started Algebra in school. > At some point, I found most of the rules similar enough, and didn't > have any problem with them. > > However, in textbook notation, if you put some expression, a > horizontal bar, and another expression below, the upper and > lower expressions are evaluated before the division (bar). > > There is no horizontal bar divide operator in Fortran, so this > problem never comes up.
Most software uses PEDMAS rules left to right but I still use brackets just in case