the question I am dealing with here is why 16 / 2 * (8 – 3 * (4 – 2)) +
1 evaluates to 17, not 5, as some have suggested, and why this is a de
facto convention nowadays.
I am all in favor of understanding, so where is your problem?
Michael
Vinaire wrote:
> No rules substitute proper understanding. A rule works 100% of the
> time only when one totally understands how it was derived in the first
> place.
>
> Today's trend appears to be toward robotic application of rules
> without understanding. Understanding is considered to be "too complex."
>
> Anything that is not understood would appear complex. Bad education
> will make most data appear very complex. With the advent of
> calculators, schools no longer teach mental math. So, we encourage a
> push-button mode of thinking, rather than a systematic thinking mode.
>
> Computers are a boon, but let us not depend upon them so much that we
> dumb down the development of thinking ability in our education.
>
> Vinaire
>
> ----- Original Message ----
> From: Michael S. <M.Suesserott@gmx.net>
> To: Math4u@yahoogroups.com
> Sent: Tuesday, December 11, 2007 2:52:51 PM
> Subject: [Math4u] 16 / 2 * (8 – 3 * (4 – 2)) + 1 Again - A Word on
> Evaluation Order
>
> There still seems to be some confusion as to the correct order of
> arithmetic operations. Having been involved in the implementation of
> computer languages in my professional career, perhaps I may be able to
> shed some light on this.
>
> It is true that there are several conventions that have been handed down
> to us from the olden days. Among them are
> the "My Dear Aunt Sally" convention (multiplication, division, addition,
> subtraction) and the "BODMAS" convention (bracketed operations,
> division, multiplication, addition, subtraction). These two, though
> different, each had a large following among mathematicians. Then, more
> than 50 years ago, with the ascent of computers, another convention
> became prevalent, one that was deemed the most straightforward to
> implement in machine and assembly language. It was the
> precedence/associativity convention that is being used today in
> practically all computer languages on the planet, and, in consequence,
> in software products such as Excel.
>
> IMHO, mathematics teachers of this present generation have a
> responsibility to teach their students what is actually being used by
> the overwhelming majority of people. Some two billion computers and
> about one billion mobile phones have been sold worldwide. C, C++, Java,
> Python, etc. are the languages used to create the software for them,
> such as Excel which is used in countless technical and commercial
> applications. All of these abide by the precedence/associativity
> convention. Nobody cares about My Dear Aunt Sally any more.
>
> How is it that Google comes up with 17 when you input 16/2(8-3(4-2))+1 ?
> The Google user interface is programmed, to a large degree, in Python,
> and of course Python obeys precedence/associativity.
>
> If PurpleMath promulgate a different standard, they are doing their
> users a grave disservice. These users will be rudely surprised when they
> find out that what they learned there is not what the real world follows.
>
> Our respected moderator, Brian, wrote he was waiting for "some authority
> such as the American Mathematical Society" to issue a convention. I
> don't think this is likely to happen. Mathematicians are, in a sense, a
> very liberal lot. As long as a definition is logically consistent, it is
> OK for them to use. Let me give you an example.
>
> If you read a mathematical paper on advanced algebra or topology topics,
> one of the first things you have to find out is the convention this
> author uses for function concatenation. Does (f o g)(x) equal f(g(x)) or
> g(f(x))? No divine decree has ever been issued from heaven, or, failing
> that, from the AMS, forcing an author to use one convention over the
> other. Both are acceptable, and both are being used to this day in
> scientific literature.
>
> In looking for a de facto standard, aside from considering what Excel
> and Google do, in things mathematical you might look at MATHEMATICA
> (www.wolfram.com <http://www.wolfram.com/>) for guidance. This is the
> most respected software in
> the field. We'll leave the question which convention MATHEMATICA follows
> as an exercise for the reader. Hint: It's not "My Dear Aunt Sally." :-)
>
> Hope this helps a little.
>
> Michael
>
>
>
>
>
> Yahoo! Groups Links
>
>
> mailto:Math4u-fullfeatured@yahoogroups.com
> <mailto:Math4u-fullfeatured@yahoogroups.com>
>
>
>
>
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