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 2021-09-28, 14:05 #1 pepi37     Dec 2011 After milion nines:) 151410 Posts 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?
 2021-09-28, 14:20 #2 kruoli     "Oliver" Sep 2017 Porta Westfalica, DE 17228 Posts 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.
2021-09-28, 14:24   #3
axn

Jun 2003

23·233 Posts

Quote:
 Originally Posted by pepi37 Since I presume this task can only have one correct answer
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 8 / 2 * (2+2) or
Code:
  8
------
2(2+2)
The way it is written, it is neither, so we need to pick an interpretation. Hence the differing answers

 2021-09-28, 19:27 #4 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 231378 Posts 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: "behead not pardon" Imagine the confusion of the "project managers" of that time.
2021-09-28, 20:32   #5
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

2×19×59 Posts

Mathematics is way too old and too perfect for such ambiguity:
Quote:
 Parentheses (simplify inside 'em) Exponents Multiplication and Division (from left to right) Addition and Subtraction (from left to right)
https://www.purplemath.com/modules/orderops.htm

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

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]
https://en.wikipedia.org/wiki/Order_...multiplication

Last fiddled with by a1call on 2021-09-28 at 20:45

2021-09-29, 00:31   #6
Dr Sardonicus

Feb 2017
Nowhere

132148 Posts

Quote:
 Originally Posted by a1call or just use Pari-gp, it will give you only the correct answer.
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)
--------------------------------------^-----

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

 2021-09-29, 09:00 #7 S485122     "Jacob" Sep 2006 Brussels, Belgium 111000011102 Posts 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.
 2021-09-29, 10:10 #8 kruoli     "Oliver" Sep 2017 Porta Westfalica, DE 17228 Posts 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. Last fiddled with by kruoli on 2021-09-29 at 10:13 Reason: Additions.
 2021-09-29, 13:46 #9 Dobri   "刀-比-日" May 2018 4758 Posts The answer could also be {8} for a finite set containing one element in the range 8 ÷ 8 from 8 to 8. "In Italy, Poland and Russia, this notation is sometimes used in engineering to denote a range of values." https://en.wikipedia.org/wiki/Obelus
2021-09-30, 12:06   #10
Dr Sardonicus

Feb 2017
Nowhere

22×3×13×37 Posts

Quote:
 Originally Posted by Batalov 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: "behead not pardon" Imagine the confusion of the "project managers" of that time.
This is a case where punctuation really would be a matter of life and death! "Behead, not pardon" and "Behead not, pardon" have opposite meanings.

 2021-09-30, 14:16 #11 pepi37     Dec 2011 After milion nines:) 2·757 Posts I am very disappointed. I expected the math to be a little better defined after all :)

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