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-   -   8 ÷ 2 (2 + 2) (https://www.mersenneforum.org/showthread.php?t=27166)

 pepi37 2021-09-28 14:05

8 ÷ 2 (2 + 2)

One group of people say result is 16 another group answer is 1
Since I presume this task can only have one correct answer , what that answer will be?

 kruoli 2021-09-28 14:20

It can have either of your solutions depending on your choice of operator precedences. (Even more if you allow more peculiar definitions.) I personally would give an implicit multiplication a higher precedence than an explicit one, since the bracket expression is visually grouped with the prefactor. But I never saw that formalised, since it is usually only a shorthand - and in this case they would be of equal precedence. Having said that, if somebody writes an expression like this, it is definitely misleading, maybe deliberately.

 axn 2021-09-28 14:24

Wrong. The expression is ambiguous. Hence there can be more than one answer depending on how you interpret.

The ambiguity is due to two incompatible notation styles being used together. Here, the multiplication operator is implicit, but the division operator is explicit. Due to this, we could reasonably interpret as meaning [C]8 / 2 * (2+2)[/C] or
[CODE]
8
------
2(2+2)[/CODE]

The way it is written, it is neither, so we need to pick an interpretation. Hence the differing answers

 Batalov 2021-09-28 19:27

Welcome to the world of semantics!

It is the same as (it sounds better in Russian) a some king's ruling that was passed down to minions:
Imagine the confusion of the "[I]project managers[/I]" of that time.

 a1call 2021-09-28 20:32

Mathematics is way too old and too perfect for such ambiguity:
[QUOTE]Parentheses (simplify inside 'em)
Exponents
Multiplication and Division ([B]from left to right[/B])
Addition and Subtraction ([B]from left to right[/B])[/QUOTE]

[url]https://www.purplemath.com/modules/orderops.htm[/url]

or just use Pari-gp, it will give you only the correct answer. :smile:

Of course you an always rely on Wikipedia to corrupt a beautiful science to nonsense. Democratic sciences anyone?

[QUOTE]
Similarly, there can be ambiguity in the use of the slash symbol / in expressions such as 1/2n.[12] If one rewrites this expression as 1 ÷ 2n and then interprets the division symbol as indicating multiplication by the reciprocal, this becomes:

1 ÷ 2 × n = 1 ×
1
/
2
× n =
1
/
2
× n.
With this interpretation 1 ÷ 2n is equal to (1 ÷ 2)n.[1][8] However, in some of the academic literature, multiplication denoted by juxtaposition (also known as implied multiplication) is interpreted as having higher precedence than division, so that 1 ÷ 2n equals 1 ÷ (2n), not (1 ÷ 2)n. For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division with a slash,[22] and this is also the convention observed in prominent physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics.[d]
[/QUOTE]

[url]https://en.wikipedia.org/wiki/Order_of_operations#Mixed_division_and_multiplication[/url]

 Dr Sardonicus 2021-09-29 00:31

[QUOTE=a1call;588930]<snip>
or just use Pari-gp, it will give you only the correct answer. :smile:
<snip>[/QUOTE]The "right answer" then, is "This doesn't parse." The problem is there's no operator between the 2 and the (.

In the error message, the ^ appeared directly under the (. I tried to put it there by inserting - characters, but YMMV.

[code]? 8/2(2+2)
*** unused characters: 8/2(2+2)
--------------------------------------^-----

? [/code]If you input 8/2*(2+2) Pari-GP gives 16.

 S485122 2021-09-29 09:00

IMHO the rule that implicit multiplication should have a higher priority is nonsense : if the sign for a multiplication operation can be omitted, there is still a multiplication to do. Why treat it differently from a multiplication which does use a sign ?

The left to right convention is simple and unambiguous.

 kruoli 2021-09-29 10:10

Let's take the example of a1call:
Why should someone interpret 1 ÷ 2n as (1 ÷ 2)n i.e. half n? This is really counterintuitive. Giving the implicit operator precedence is also unambiguous, maybe even simpler and definitely self-evident.

Edit: Why should we treat something that is written differently inevitably the same? Math is not a conversational language which may have ambiguities etc., math should be well defined and having multiple ways to express the exact same thing is not helpful.

 Dobri 2021-09-29 13:46

The answer could also be [B]{8}[/B] for a finite set containing one element [U]in the range [/U][U][U][FONT=&quot]8[/FONT][/U][FONT=&quot] ÷ [U]8 [/U][/FONT]from 8 to 8[/U].
"[FONT=&quot]In Italy, Poland and Russia, this notation is sometimes used in engineering to denote [U][B]a range of values[/B][/U].[/FONT]"
[URL]https://en.wikipedia.org/wiki/Obelus[/URL]

 Dr Sardonicus 2021-09-30 12:06

[QUOTE=Batalov;588925]Welcome to the world of semantics!

It is the same as (it sounds better in Russian) a some king's ruling that was passed down to minions: