Re: [Math4u] Re: 16 / 2 * (8 – 3 * (4 – 2)) + 1 Again - A Word on Evaluation Order

I am not expecting the world to change with what I say. I am just working with those students who would like to apply mathematical thinking with understanding and ease. :)

 

Vinaire

----- Original Message ----
From: Brian Edward Jensen <brianejensen@prodigy.net>
To: Math4u@yahoogroups.com
Sent: Tuesday, December 18, 2007 4:30:30 PM
Subject: [Math4u] Re: 16 / 2 * (8 â€" 3 * (4 â€" 2)) + 1 Again - A Word on Evaluation Order

Yes, #1 is a standard interpretation. (We have learned that there are
other interpretations being debated.) If you want to dream up other
ways that get the same answer, fine. You can say, "Here's another way
that gets the correct answer." But please don't say the world must
change the standard interpretation to your method. Sometimes your
method is easier to calculate as you have shown. But you have also
shown that it causes enormous confusion. Your interpretation requires
more rules which you make up as you go along to replace one simpler
rule. Plus adding one more method of Evaluation (which is inferior)
greatly confuses the issue.

Regards,

Brian

--- In Math4u@yahoogroups. com, Vinaire <vinaire@... > wrote:
>
> I agree I need to express my thoughts more clearly. For now I shall
just stick to the following facts.
>
> 1. When addition and subtraction are present together they may
be carried out from left to right in that sequence.
> 2. An operation on the right may be carried out first only
when there is addition on its left.
> 3. Mistakes are likely when an operation on the right is
carried out first with subtraction on its left.
>
> I never said addition and subraction are of the same precedence.
They are of the same order.
>
> Where log and exponentiation are concerned I would use parentheses
as follows:
>
> (log 10) ^ 2 or log (10^2) to avoid confusion.
>
> Ultimately, it is a matter of agreed upon communication.
>
> Vinaire
>
>
>
> ----- Original Message ----
> From: Rob van Wijk <robvanwijk@ ...>
> To: Math4u@yahoogroups. com
> Sent: Monday, December 17, 2007 4:32:09 PM
> Subject: Re: [Math4u] 16 / 2 * (8 â€" 3 * (4 â€" 2)) + 1 Again - A
Word on Evaluation Order
>
>
> Comments inside
>
> -------- Original-Nachricht --------
> > Datum: Wed, 12 Dec 2007 07:24:09 -0800 (PST)
> > Von: Vinaire <vinaire@yahoo. com>
> > An: Math4u@yahoogroups. com
> > Betreff: Re: [Math4u] 16 / 2 * (8 â€" 3 * (4 â€" 2)) + 1 Again -
A Word on Evaluation Order
>
> > Addition and subtraction are inverse of each other, but
subtraction is
> > more complex because, initially, it was subtraction that led to
the idea
> > of negative numbers, and expanded the understanding in terms of
integers.
> > Subtraction, thus, takes precedence over addition.
>
> Substraction takes precedence over addition /because/ it led to
discovery
> if negative numbers? Sorry, but I hope you're not serious. (This
remark is
> entirely seperate from me (and apparently, the rest of the world)
still not
> agreeing with the fact that substraction would take precedence in
the first
> place.)
>
> > Multiplication is "compressed addition." One multiplication
consists of
> > several additions. Therefore, multiplication is an "order of
maginitude"
> > higher than addition. Because, addition and subtraction are of
the same
> > order, multiplication takes precedence over both subtraction and
> > addition.
>
> How come add and sub are same precedence all of a sudden?
> I agree with the fact that mult takes precedence over add and sub.
I'm not
> sure if the reason why is correct, but I'll admit it sounds
plausible.
>
> > Division is inverse of multiplication, but division is more
complex
> > because, initially, it was division that led to the idea of
fractions,
> > and expanded the understanding in terms of rational numbers.
Division,
> > thus, takes precednece over multiplication.
>
> See my disagreement with "sub takes precedence over add".
>
> > Exponents being "compressed multiplication" are of a higher order
of
> > operation than multiplication and division...
>
> See my (second) remark about "mult precedence over add and sub".
>
> > Logarithms are inverse of exponents, but more complex...
>
> Okay, so according to the entire reasoning of the email, you'd have
to say
> that log would take precedence over exponentation, right? Then that
would
> mean "log 10 ^ 2" would be evaluated as (log 10) ^ 2 =~ 1^2 =~ 1,
right?
>
> http://www.google. com/search? q=log+10% 5E2
>
> says it should be (and I completely agree) log (10 ^ 2) = log 100 =
2
>
> > I hope you got the point now, and you can fill in the rest.
>
> Could you /please/ just accept that the convention used all over
the world
> is not what you'd like it to be / you think it is? Thank you!
>
> > Vinaire
>
> Grtz,
> Rob
>
> --
> Psssst! Schon vom neuen GMX MultiMessenger gehört?
> Der kann`s mit allen: http://www.gmx. net/de/go/ multimessenger?
did=10
>
>
>
>
>
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