What is this "order of operation" cult now with math?

[Vtile]

I just came across a two days ago with this '8/2(2+2)=?'

Well I had to say that I'm honestly really perplexed with the whole PEDMAS or similar religeaus people touting this order of operation religion. It seems that only thing that matters is this order of operation acronym and rest of the superset rules are thrown where light do not shine.

..But the expression is staged for trolling, but the last nail to the coffin is the fact that wolfram alpha is giving the absolutely wrong answer instead of the better "invalid formatting" than HP48 (Droid48 for android) gives (as for a computer).

Edit. Ps. Subject seems to be semantic war between different branches of mathematics.

[Maximilian Hohmann]

Hello!

(04-03-2021 06:47 PM)Vtile Wrote:  ... the fact that wolfram alpha is giving the absolutely wrong answer ...

No, Wolfram Alpha gives the correct answer. And I don't see anything wrong with that expression either, provided that the omission of an operator is implicitly interpreted as multiplication. This is how I was taught both at school and university. In Italy and Germany, but more than 30 years ago. Maybe things are different today.

Regards
Max

[Steve Simpkin]

(04-03-2021 06:47 PM)Vtile Wrote:  I just came across a two days ago with this '8/2(2+2)=?'

Well I had to say that I'm honestly really perplexed with the whole PEDMAS or similar religeaus people touting this order of operation religion. It seems that only thing that matters is this order of operation acronym and rest of the superset rules are thrown where light do not shine.

..But the expression is staged for trolling, but the last nail to the coffin is the fact that wolfram alpha is giving the absolutely wrong answer instead of the better "invalid formatting" than HP48 gives (as for a computer).

Yes. Either it should be made illegal across the entire world to write an equation like this or there should be an 11th Commandment passed down to deal with it. If for no other reason than so we don't have to have these endless debates about who is right.

https://www.hpmuseum.org/forum/thread-11...eration%22

https://www.hpmuseum.org/forum/thread-8982.html

https://www.hpmuseum.org/cgi-sys/cgiwrap...ead=246984

[Vtile]

I must disagree. The sole reason is the 1st axiom of real number algebra (and therefore also aplying to subsets) and the distributive theorem and how the convention is to mark the common factor without operator to parentheses (as is done with ie. exponentation) that is to interpret the whole right side notation in this case as a one object as '(a(X+Y))'.

Can't say what is thought for me been under too many influential teachers and institutions along the years. As in Finland.

[Vtile]

(04-03-2021 07:32 PM)Steve Simpkin Wrote:  

(04-03-2021 06:47 PM)Vtile Wrote:  I just came across a two days ago with this '8/2(2+2)=?'

Well I had to say that I'm honestly really perplexed with the whole PEDMAS or similar religeaus people touting this order of operation religion. It seems that only thing that matters is this order of operation acronym and rest of the superset rules are thrown where light do not shine.

..But the expression is staged for trolling, but the last nail to the coffin is the fact that wolfram alpha is giving the absolutely wrong answer instead of the better "invalid formatting" than HP48 gives (as for a computer).

Yes. Either it should be made illegal across the entire world to write an equation like this or there should be an 11th Commandment passed down to deal with it. If for no other reason than so we don't have to have these endless debates about who is right.

https://www.hpmuseum.org/forum/thread-11...eration%22

https://www.hpmuseum.org/forum/thread-8982.html

https://www.hpmuseum.org/cgi-sys/cgiwrap...ead=246984

I see, I should have used a search. I think we should make infix illegal for whole world.

Which leads to my distaste of (basic) mathematics as subject, until found the RPN which made it logical and enjoy to use once again. Łukasiewicz were indeed right.

[Steve Simpkin]

(04-03-2021 07:48 PM)Vtile Wrote:  I see, I should have used a search. I think we should make infix illegal for whole world.

Which leads to my distaste of (basic) mathematics as subject, until found the RPN which made it logical and enjoy to use once again. Łukasiewicz were indeed right.

LOL Yes but RPN would not really help us for this case. It would just make us responsible for deciding what order to solve the equation. I have seen this type of badly written equation debated, often with religious fervor, by many people with roughly half coming up with one answer and the other half with a different answer. That is the very definition of ambiguous. Many people assume the way they were taught to solve such a poorly written problem is the one and only "true" way not realizing that others may have been taught differently. It doesn't help that algebraic calculator manufacturers have implemented different interpretations for this form of equation and have sometimes changed their minds with different models.

   
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I think the lesson to be learned here is to avoid writing an equation is such a way that it can be interpreted differently by people. An extra set of parentheses in this case would make your intentions clear to *everyone* with nothing to debate.

[Massimo Gnerucci]

(04-03-2021 09:49 PM)Steve Simpkin Wrote:  I think the lesson to be learned here is to avoid writing an equation is such a way that it can be interpreted differently by people. An extra set of parentheses in this case would make your intentions clear to *everyone* with nothing to debate.

Ditto.

[Vtile]

(04-03-2021 10:07 PM)Massimo Gnerucci Wrote:  

(04-03-2021 09:49 PM)Steve Simpkin Wrote:  I think the lesson to be learned here is to avoid writing an equation is such a way that it can be interpreted differently by people. An extra set of parentheses in this case would make your intentions clear to *everyone* with nothing to debate.

Ditto.

I do agree..

But,
Not so hastily .. eddie shore wrote an excellent philosophical question 2nd last post of linked threads.. The question was, should calculators accept implicid operators at all?

My annoyance of wolfram alpha as it tries to be the the mathematical scientific database is that it do not not give any form of indication of ambiqyity.

[Vtile]

(04-03-2021 09:49 PM)Steve Simpkin Wrote:  

(04-03-2021 07:48 PM)Vtile Wrote:  I see, I should have used a search. I think we should make infix illegal for whole world.

Which leads to my distaste of (basic) mathematics as subject, until found the RPN which made it logical and enjoy to use once again. Łukasiewicz were indeed right.

LOL Yes but RPN would not really help us for this case. It would just make us responsible for deciding what order to solve the equation.

Hehe. Don't change forget that the infix would be banned so we would not need this kind of semantic discussion arising from invisible brackets and transformation from superior written format to lesser typed format (both algebraig).

There would not be floating around 8/2(2+2)=? questions.
There would be something like:
8 2 / 2 2 + × = ?
8 2 2 2 + × / = ?
Without amquity. ..and because no ambiquity these would have no value of arising depate.

..and since these would be notation learned from the beginning it would be as expressive as now is written algebraic format.

That is if Lucasevich was absolutely right.
?

[Vtile]

A question. What is the relation here about two things a fractio s vs multiplication they are the same thing, but it seems that in some schooling paths the division and fraction is given difference by mixed division symbols (non universal marking)?
This is/was problematic before UTF8, typesets might had or might not had two division symbols.

If we assume fractions as an object (I can't remember what was the algebraic equivalent word) written with symbol '/' and all other divisions with this 'minus with dots', then the interpretation of 16 will be much more understandable with applying the O.O.O. Still this is interpretation question, not as much mathematics rules.

Personally I need to remember to draw the ambiquity card if I find myself sitting to some official examination with this kind of 1-line questions at future. Btw. I can remember this ambiquity thing was a common place at highschool (and after) and if exams had ambiquity found by students it would be removed from exam or corrected by teacher at examination.

[Massimo Gnerucci]

(04-04-2021 11:50 AM)Vtile Wrote:  all other divisions with this 'minus with dots',

Do you mean the obelus?
÷ U+00F7

[Vtile]

(04-04-2021 12:41 PM)Massimo Gnerucci Wrote:  

(04-04-2021 11:50 AM)Vtile Wrote:  all other divisions with this 'minus with dots',

Do you mean the obelus?
÷ U+00F7

Yes I did mean obelus.

I'm not sure how these one line expressions were written here and what might be the current agreement, the official (by linquistics that is) symbol for division was Colon IIRC. Which seems to be in ie. US symbol for ratios.

I'm using solely my cell phone, so I'm a bit restricted at editing.

[Vtile]

This is a really nice overview of the subject in view of calculators and textbooks.
https://youtu.be/4x-BcYCiKCk

[Gerald H]

Basic problem is the avoidance of masses of brackets confusing animal minds, leading to conventions to weed out "unnecessary" uses.

If only someone could invent a notation dispensing with brackets & manifesting clarity - the World awaits such a measure.

[Vtile]

For me it seems that this confusion or split have become true when people started to interface with computers (parsing classic paper infix notation with hidden brackets and many times 2-dimensions for computer 1-dimensional entry) and then with bedacocy justification some group got the idea that pupils should be prepared for computers, because computers are scary and stupid. Soup was set.

Now it seems that there is loosely a two and half groups.
The ones that read one line expressions like computer (but adding hidden symbols, which compilers do not do)
The ones that read one line expression like it was a print paper.
The last half that try to deduct the right aproach from content or say directly that something is ambiqyous. (Most math. uni. Profs seems to be on this group, which is wise I must admit[/b].)

[toml_12953]

(04-05-2021 09:39 AM)Vtile Wrote:  For me it seems that this confusion or split have become true when people started to interface with computers (parsing classic paper infix notation with hidden brackets and many times 2-dimensions for computer 1-dimensional entry) and then with bedacocy justification some group got the idea that pupils should be prepared for computers, because computers are scary and stupid. Soup was set.

Now it seems that there is loosely a two and half groups.
The ones that read one line expressions like computer (but adding hidden symbols, which compilers do not do)
The ones that read one line expression like it was a print paper.
The last half that try to deduct the right aproach from content or say directly that something is ambiqyous. (Most math. uni. Profs seems to be on this group, which is wise I must admit[/b].)

We were always taught that implied multiplication is still multiplication so it's treated the same as if the multiplication symbol is in there and is at the same priority level as division.

[Vtile]

(04-05-2021 11:03 PM)toml_12953 Wrote:  

(04-05-2021 09:39 AM)Vtile Wrote:  For me it seems that this confusion or split have become true when people started to interface with computers (parsing classic paper infix notation with hidden brackets and many times 2-dimensions for computer 1-dimensional entry) and then with bedacocy justification some group got the idea that pupils should be prepared for computers, because computers are scary and stupid. Soup was set.

Now it seems that there is loosely a two and half groups.
The ones that read one line expressions like computer (but adding hidden symbols, which compilers do not do)
The ones that read one line expression like it was a print paper.
The last half that try to deduct the right aproach from content or say directly that something is ambiqyous. (Most math. uni. Profs seems to be on this group, which is wise I must admit[/b].)

We were always taught that implied multiplication is still multiplication so it's treated the same as if the multiplication symbol is in there and is at the same priority level as division.

I think I have thought something similar at least the hierarchy is the same as in most countries, but the only difference seems to be this implied multiplication and how it groups things together and I don't think that any teacher is pushed it at all, it just have been naturally formed .. maybe?

If I do see one line expression like:
\begin{equation}
1(3-1)/2(1+1)
\end{equation}

..the expression I do actually instantly internalize and see is:
\begin{equation}
\frac{1(3-1)}{2(1+1)}
\end{equation}

Nothing like this:
\begin{equation}
\frac{1(3-1)}{2}\times (1+1)
\end{equation}

Or not even this:
\begin{equation}
\frac{1(3-1)(1+1)}{2}
\end{equation}

...And definitely not:
\begin{equation}
EVAL(3-1)
\end{equation}

Unfortunately this doesn't have enough daylight that there actually is more than one way to analyse these. For me now that I have studied a bit on the subject I'm more aware of this and will use for the future the ambiguous card, since both have their merits, while I do personally lean the side of implied multiplication grouping (...for human consumed expressions, compilers have manuals).

[Ren]

I've thought of mathematics as an "exact" science.
To see such difference of opinion about something as "critical" as this, saddens me.
(or maybe I've forgotten to take an anti-depressant lately B^)

[Maximilian Hohmann]

Hello!

(04-08-2021 05:16 PM)Ren Wrote:  I've thought of mathematics as an "exact" science.

It is an exact science as long as unambiguous notation is used. Examples like this one help to uncover the few remaining ambiguities. If people learn from it...

If you write down the equations required to land a rover on Mars then don't be shy to use some extra parentheses. Maybe the equation does not look as pretty as it could, but who really cares?

Regards
Max

[Albert Chan]

(04-08-2021 05:34 PM)Maximilian Hohmann Wrote:  

(04-08-2021 05:16 PM)Ren Wrote:  I've thought of mathematics as an "exact" science.

It is an exact science as long as unambiguous notation is used.

Quote from the video: "it depends who you are talking to ... "