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

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@gmx.net>
To: Math4u@yahoogroups.com
Sent: Monday, December 17, 2007 4:32:09 PM
Subject: Re: [Math4u] 16 / 2 * (8 – 3 * (4 – 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 – 3 * (4 – 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

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