BIMDAS - Order of Calculation
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From: Ken Russell on 22 Feb 2005 01:33 -3^2 is the same as -3*-3 which equals 9 not -9 At least that's what I was taught over 60 years ago. -- Ken Russell kenrussellyourhat(a)optushome.com.au Remove yourhat to reply by e-mail .. "Atreides" <atreides1AThotmailD0Tcom> wrote in message news:C60BB320-A11E-4E81-87E3-52C3C407ED18(a)microsoft.com... > I've recently noticed that Excel flies in the face of standard scientific, > mathematical and engineering convention in the calculation of powers for > numbers that are then multiplied by a negative. > > The convention of mathematics, "BIMDAS" (or similar acronyms), states that > _I_ndices (or powers, or exponents), should be calculated before > _M_ultiplication. Because of this, the following is accepted as correct: > > -3^2 = -9. > > This is because it is the equivalent of (-1) * 3^2 = -1 * 9 = -9 > > However, Excel chooses to recognise this as (-3)^2 = 9. > > This error is particularly problematic when doing algebraic computations > in > such a tool as Mathematica and then copying the result into Excel in input > form. That is, > > -x^2 -> -A1^2 > -> -A1^2 > (Mathematica) (Mathematica with reference substituted) (Excel) > > To correct the error, one must manually change it to: -(A1^2) > > QUESTIONS > 1: Why does Excel have this convention! > 2: Is there any way to change it/make is more convenient? > > I've only recently noticed this (which is quite scary to think how many > errors I may have made in the past!) > > Thanks for your time, > > Cheers, > Peter
From: Atreides on 22 Feb 2005 01:43 But then Ken, what reason would one have for writing: -x^2 if it really simplifies down to -x * -x = x^2? How would one write the opposite of the square of x? Cheers, Peter "Ken Russell" wrote: > -3^2 is the same as -3*-3 which equals 9 not -9 > > At least that's what I was taught over 60 years ago. > > -- > Ken Russell > > kenrussellyourhat(a)optushome.com.au > Remove yourhat to reply by e-mail > .. > > "Atreides" <atreides1AThotmailD0Tcom> wrote in message > news:C60BB320-A11E-4E81-87E3-52C3C407ED18(a)microsoft.com... > > I've recently noticed that Excel flies in the face of standard scientific, > > mathematical and engineering convention in the calculation of powers for > > numbers that are then multiplied by a negative. > > > > The convention of mathematics, "BIMDAS" (or similar acronyms), states that > > _I_ndices (or powers, or exponents), should be calculated before > > _M_ultiplication. Because of this, the following is accepted as correct: > > > > -3^2 = -9. > > > > This is because it is the equivalent of (-1) * 3^2 = -1 * 9 = -9 > > > > However, Excel chooses to recognise this as (-3)^2 = 9. > > > > This error is particularly problematic when doing algebraic computations > > in > > such a tool as Mathematica and then copying the result into Excel in input > > form. That is, > > > > -x^2 -> -A1^2 > > -> -A1^2 > > (Mathematica) (Mathematica with reference substituted) (Excel) > > > > To correct the error, one must manually change it to: -(A1^2) > > > > QUESTIONS > > 1: Why does Excel have this convention! > > 2: Is there any way to change it/make is more convenient? > > > > I've only recently noticed this (which is quite scary to think how many > > errors I may have made in the past!) > > > > Thanks for your time, > > > > Cheers, > > Peter > > >
From: Ken Russell on 22 Feb 2005 02:04 Doesn't -(x^2) satisfy -9? -- Ken Russell kenrussellyourhat(a)optushome.com.au Remove yourhat to reply by e-mail .. "Atreides" <atreides1AThotmailD0Tcom> wrote in message news:26D8CA4A-B270-4F63-A7EB-1C1215CFF0CF(a)microsoft.com... > But then Ken, what reason would one have for writing: > > -x^2 > > if it really simplifies down to -x * -x = x^2? > > How would one write the opposite of the square of x? > > Cheers, > Peter > > > "Ken Russell" wrote: > >> -3^2 is the same as -3*-3 which equals 9 not -9 >> >> At least that's what I was taught over 60 years ago. >> >> -- >> Ken Russell >> >> kenrussellyourhat(a)optushome.com.au >> Remove yourhat to reply by e-mail >> .. >> >> "Atreides" <atreides1AThotmailD0Tcom> wrote in message >> news:C60BB320-A11E-4E81-87E3-52C3C407ED18(a)microsoft.com... >> > I've recently noticed that Excel flies in the face of standard >> > scientific, >> > mathematical and engineering convention in the calculation of powers >> > for >> > numbers that are then multiplied by a negative. >> > >> > The convention of mathematics, "BIMDAS" (or similar acronyms), states >> > that >> > _I_ndices (or powers, or exponents), should be calculated before >> > _M_ultiplication. Because of this, the following is accepted as >> > correct: >> > >> > -3^2 = -9. >> > >> > This is because it is the equivalent of (-1) * 3^2 = -1 * 9 = -9 >> > >> > However, Excel chooses to recognise this as (-3)^2 = 9. >> > >> > This error is particularly problematic when doing algebraic >> > computations >> > in >> > such a tool as Mathematica and then copying the result into Excel in >> > input >> > form. That is, >> > >> > -x^2 -> -A1^2 >> > -> -A1^2 >> > (Mathematica) (Mathematica with reference substituted) >> > (Excel) >> > >> > To correct the error, one must manually change it to: -(A1^2) >> > >> > QUESTIONS >> > 1: Why does Excel have this convention! >> > 2: Is there any way to change it/make is more convenient? >> > >> > I've only recently noticed this (which is quite scary to think how many >> > errors I may have made in the past!) >> > >> > Thanks for your time, >> > >> > Cheers, >> > Peter >> >> >>
From: Atreides on 22 Feb 2005 02:19 > Doesn't -(x^2) satisfy -9? Yes, according to your convention, you would have to write -(x^2). So consider the two systems we could have: 1. x^2 the opposite of which is -x^2 2. x^2 the opposite of which is -(x^2) System number one (which, in my experience, is standard in maths, science and engineering textbooks) makes more sense to me. Indices or powers have precedence over multiplication. Consider graphs of parabolas. According to your definition, the graphs: y = x^2 AND y = -x^2 would be the same graph. However, in my experience, eveyone knows that y = x^2 is a "U" shape while y = -x^2 is an "upsidedown-U" shape. Would you agree? Cheers, Peter "Ken Russell" wrote: > > -- > Ken Russell > > kenrussellyourhat(a)optushome.com.au > Remove yourhat to reply by e-mail > .. > > "Atreides" <atreides1AThotmailD0Tcom> wrote in message > news:26D8CA4A-B270-4F63-A7EB-1C1215CFF0CF(a)microsoft.com... > > But then Ken, what reason would one have for writing: > > > > -x^2 > > > > if it really simplifies down to -x * -x = x^2? > > > > How would one write the opposite of the square of x? > > > > Cheers, > > Peter > > > > > > "Ken Russell" wrote: > > > >> -3^2 is the same as -3*-3 which equals 9 not -9 > >> > >> At least that's what I was taught over 60 years ago. > >> > >> -- > >> Ken Russell > >> > >> kenrussellyourhat(a)optushome.com.au > >> Remove yourhat to reply by e-mail > >> .. > >> > >> "Atreides" <atreides1AThotmailD0Tcom> wrote in message > >> news:C60BB320-A11E-4E81-87E3-52C3C407ED18(a)microsoft.com... > >> > I've recently noticed that Excel flies in the face of standard > >> > scientific, > >> > mathematical and engineering convention in the calculation of powers > >> > for > >> > numbers that are then multiplied by a negative. > >> > > >> > The convention of mathematics, "BIMDAS" (or similar acronyms), states > >> > that > >> > _I_ndices (or powers, or exponents), should be calculated before > >> > _M_ultiplication. Because of this, the following is accepted as > >> > correct: > >> > > >> > -3^2 = -9. > >> > > >> > This is because it is the equivalent of (-1) * 3^2 = -1 * 9 = -9 > >> > > >> > However, Excel chooses to recognise this as (-3)^2 = 9. > >> > > >> > This error is particularly problematic when doing algebraic > >> > computations > >> > in > >> > such a tool as Mathematica and then copying the result into Excel in > >> > input > >> > form. That is, > >> > > >> > -x^2 -> -A1^2 > >> > -> -A1^2 > >> > (Mathematica) (Mathematica with reference substituted) > >> > (Excel) > >> > > >> > To correct the error, one must manually change it to: -(A1^2) > >> > > >> > QUESTIONS > >> > 1: Why does Excel have this convention! > >> > 2: Is there any way to change it/make is more convenient? > >> > > >> > I've only recently noticed this (which is quite scary to think how many > >> > errors I may have made in the past!) > >> > > >> > Thanks for your time, > >> > > >> > Cheers, > >> > Peter > >> > >> > >> > > >
From: Ken Russell on 22 Feb 2005 02:30 I am a simple man who bows to your superior knowledge. At least all my maths teachers are dead now :-) Cheers, Ken Russell kenrussellyourhat(a)optushome.com.au Remove yourhat to reply by e-mail .. "Atreides" <atreides1AThotmailD0Tcom> wrote in message news:C1F0EC25-80DC-4147-AAA6-08716511DD40(a)microsoft.com... >> Doesn't -(x^2) satisfy -9? > > Yes, according to your convention, you would have to write -(x^2). So > consider the two systems we could have: > > 1. x^2 the opposite of which is -x^2 > 2. x^2 the opposite of which is -(x^2) > > System number one (which, in my experience, is standard in maths, science > and engineering textbooks) makes more sense to me. Indices or powers have > precedence over multiplication. > > Consider graphs of parabolas. According to your definition, the graphs: > > y = x^2 > > AND > > y = -x^2 > > would be the same graph. However, in my experience, eveyone knows that y = > x^2 is a "U" shape while y = -x^2 is an "upsidedown-U" shape. > > Would you agree? > > Cheers, > Peter > > > > > > "Ken Russell" wrote: > >> >> -- >> Ken Russell >> >> kenrussellyourhat(a)optushome.com.au >> Remove yourhat to reply by e-mail >> .. >> >> "Atreides" <atreides1AThotmailD0Tcom> wrote in message >> news:26D8CA4A-B270-4F63-A7EB-1C1215CFF0CF(a)microsoft.com... >> > But then Ken, what reason would one have for writing: >> > >> > -x^2 >> > >> > if it really simplifies down to -x * -x = x^2? >> > >> > How would one write the opposite of the square of x? >> > >> > Cheers, >> > Peter >> > >> > >> > "Ken Russell" wrote: >> > >> >> -3^2 is the same as -3*-3 which equals 9 not -9 >> >> >> >> At least that's what I was taught over 60 years ago. >> >> >> >> -- >> >> Ken Russell >> >> >> >> kenrussellyourhat(a)optushome.com.au >> >> Remove yourhat to reply by e-mail >> >> .. >> >> >> >> "Atreides" <atreides1AThotmailD0Tcom> wrote in message >> >> news:C60BB320-A11E-4E81-87E3-52C3C407ED18(a)microsoft.com... >> >> > I've recently noticed that Excel flies in the face of standard >> >> > scientific, >> >> > mathematical and engineering convention in the calculation of powers >> >> > for >> >> > numbers that are then multiplied by a negative. >> >> > >> >> > The convention of mathematics, "BIMDAS" (or similar acronyms), >> >> > states >> >> > that >> >> > _I_ndices (or powers, or exponents), should be calculated before >> >> > _M_ultiplication. Because of this, the following is accepted as >> >> > correct: >> >> > >> >> > -3^2 = -9. >> >> > >> >> > This is because it is the equivalent of (-1) * 3^2 = -1 * 9 = -9 >> >> > >> >> > However, Excel chooses to recognise this as (-3)^2 = 9. >> >> > >> >> > This error is particularly problematic when doing algebraic >> >> > computations >> >> > in >> >> > such a tool as Mathematica and then copying the result into Excel in >> >> > input >> >> > form. That is, >> >> > >> >> > -x^2 -> -A1^2 >> >> > -> -A1^2 >> >> > (Mathematica) (Mathematica with reference substituted) >> >> > (Excel) >> >> > >> >> > To correct the error, one must manually change it to: -(A1^2) >> >> > >> >> > QUESTIONS >> >> > 1: Why does Excel have this convention! >> >> > 2: Is there any way to change it/make is more convenient? >> >> > >> >> > I've only recently noticed this (which is quite scary to think how >> >> > many >> >> > errors I may have made in the past!) >> >> > >> >> > Thanks for your time, >> >> > >> >> > Cheers, >> >> > Peter >> >> >> >> >> >> >> >> >>
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