Poll: Solve a simple math problem

[OldRat]

The answer is zero because the * mean times by and anything times by zero is...zero!

It would if everything but times zero was in parenthesis. Sadly, it isn't, and thus, amazingly enough, you ONLY MULTIPLY THE NUMBER THAT IS BEING MULTIPLIED. As in, the last 1. Order of operations, people.

I believe the phrase mindfuck applies here! o_0

See, I'll show you:

This is how you'd get a zero: (1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+1)*0

Note the parenthesis, meaning everything inside overrides the usual order of operations (or is the first thing in order of operations, however you prefer). This way, you would get a zero.

HOWEVER, this is not the case. The case is: 1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+1*0
No parenthesis, no special priority for the filthy masses of addition (and one miserly case of substraction)

Order of operations goes (as you really should already know and I shouldn't need to explain, since this is taught in elementary schools): parenthesis, exponents and roots, multiplication and division, and finally addition and subtraction. Going from left to right in case of equals. You solve the things in that order.

So, the first thing you solve is the multiplication. One times zero. That's zero. So the whole thing looks like this: 1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+0
And the rest is just counting 1's.

Got it now?

And on a sidenote, I'm still honestly, actually amazed people manage to screw this up. THIS, of all things. Such a simple, elementary school level thing.

 

[DanDanikov]

There's no such thing. Calculators are just tools, they do what you tell them. If you tell your calculator to do operations in a particular order, that's what it'll do, but there's nothing stopping you from telling it a different order. You're the one in control, not the calculator. It's up to you to pick the right order.

Note I said pocket calculator specifically to differentiate from more advanced scientific calculators that will allow input of the whole equation and have their own (sometimes conflicting) ideas of operator precedence.

I'm not going to insult you and call you stupid, because I refuse to believe you weren't aware of simpler calculators. I think that you deliberately are contradicting my point either to be argumentative or out of a unwillingness to concede your position. I have given you an example of how this equation can be input into a fairly standard device and give an answer that differs from your 'one and only right answer'. I will partially concede your point that calculators are mere tools and reflect the intelligence of the user, but that just returns to my original point that you have yet to refute- that the original statement was entirely unqualified and thus subject to interpretation.

Any answer must have made assumptions. Varying assumptions will give differing answers. The most popular or most conventional answer doesn't make it the sole correct answer (argumentum ad populum, a logical fallacy).

I imagine many people won't be as aware of why they're getting one answer or another, but the fact that many of them (30%) are getting an alternate does suggest there is a convention people are following that differs from your most popular one. More importantly, that convention has been previously demonstrated, explained, and is logical and consistent.

 

[WOPR]

The problem with the answer being 4 since 10-6+1*0 = 4 is that (1+1+1+1+1+1+1+1+1+1)-(1+1+1+1+1+1)+(1*0) does not equal the original problem. The -(1+1+1+1+1+1) part is the same as (-1)*(1+1+1+1+1+1) which equals(-1-1-1-1-1-1). Therefore (1+1+1+1+1+1+1+1+1+1)-(1+1+1+1+1+1)+(1*0) = 1+1+1+1+1+1+1+1+1+1-1-1-1-1-1-1+1*0, which is completely different than the original.

Learn your math, Add/Subtract and Multiply/Divide are interchangeable operations that go in left to right orther (unless there are parenthesis)

meaning
(1+1+1+1+1+1+1+1+1)+(1-1)+(1+1+1+1+1)+(1*0)
would be a better operation
(again the answer is 14)
Odd how half of the people to answer this can get it wrong
...when this is something I can find in a third (or forth) grade math book

 

[Harlief]

This equation could definitely use some [brackets] for purposes of clarity.

Could it have been written more clearly? Yes.
Did it need to have been written more clearly? NO!

Chill, I'm only offering my opinion; there's no need for shouting.
It's my opinion that if an equation can be written more clearly, then it should be because people have a habit of screwing up unnecessarily complicated mental arithmetic.
This will be my last say on the matter because I'm clearly getting you over-excited.

 

[Shreddie]

The problem with the answer being 4 since 10-6+1*0 = 4 is that (1+1+1+1+1+1+1+1+1+1)-(1+1+1+1+1+1)+(1*0) does not equal the original problem. The -(1+1+1+1+1+1) part is the same as (-1)*(1+1+1+1+1+1) which equals(-1-1-1-1-1-1). Therefore (1+1+1+1+1+1+1+1+1+1)-(1+1+1+1+1+1)+(1*0) = 1+1+1+1+1+1+1+1+1+1-1-1-1-1-1-1+1*0, which is completely different than the original.

Learn your math, Add/Subtract and Multiply/Divide are interchangeable operations that go in left to right orther (unless there are parenthesis)

meaning
(1+1+1+1+1+1+1+1+1)+(1-1)+(1+1+1+1+1)+(1*0)
would be a better operation
(again the answer is 14)
Odd how half of the people to answer this can get it wrong
...when this is something I can find in a third (or forth) grade math book

I think you may have misunderstood what I was trying to say. I know the answer is 14, but I noticed a lot of people arguing that the answer was 4 and they were the ones who arranged the problem like (1+1+1+1+1+1+1+1+1+1)-(1+1+1+1+1+1)+(1*0). I was trying to show why that is wrong. Also, the comment was supposed to be a quote but for some reason that didn't happen and it probably ended up not making much sense.

 

[Maze1125]

The most popular or most conventional answer doesn't make it the sole correct answer (argumentum ad populum, a logical fallacy).

I'm going to address this specific part because it addresses the point as a whole.

The standard method is the correct one because most people use it, and that is not a logical fallacy.

Why? Because it is a matter of definition. The signs are used that way because that is how they are defined. There is nothing wrong with using a different definition, but if you do, then you have to explicitly say, if you do not specify what definition you are using then it is assumed that you are using the standard one.

That is true of every part of human communication. If you use a non-standard definition without clarification then you are being either obtuse or ignorant.

The original question does not clarify, therefore the standard is assumed. If you answer in a non-standard way, without clarification, then you are simply wrong.

 

[WOPR]

*snip*

Ahh, alright then, sorry about that, I'm just really really sleepy haha

but yeah, I showed that problem to a bunch of my college friends and out of the 25 or so I showed, only 2 got it right, everyone else "ZERO!" me "Nope" them "OH WAIT UHHH..." (then said either 16, 4, or "it is too 0 you douche! I hate math!")

 

[madwarper]

It's my opinion that if an equation can be written more clearly,

Something I've already said. However, not as clear as it could be =/= complicated.

then it should be because people have a habit of screwing up unnecessarily complicated mental arithmetic.

There's nothing complicated about this. It's just a little order of operations using only simple Multiplication, Addition and Subtraction.

So far, the wrong answers are from a) not following the rules of operations (leading to 0), b) not understanding that multiplication/division and addition/subtraction are the same thing (leading to 4), or making simple mistakes (leading to most other answers).

The most popular or most conventional answer doesn't make it the sole correct answer (argumentum ad populum, a logical fallacy).

The standard method is the correct one because most people use it, and that is not a logical fallacy.

I think you're missing the point...

Yes, the standard (ie. correct) method of solving the problem will only lead to the answer of 14.
What makes the correct method correct is not the fact that the most people used it. It's because it follows the laws of Math.

Let's suppose that people continue to vote for '0' and gets more votes than '14'.[footnote]even though this thread can't seem to make back to page 1, moderator hoodoo methinks[/footnote] By your logic, if and when '0' overtakes '14', the method that arrives at '0' becomes the new 'standard method', 'because most people use it'. Which, goes without saying, is wrong.

 

[DanDanikov]

The most popular or most conventional answer doesn't make it the sole correct answer (argumentum ad populum, a logical fallacy).

I'm going to address this specific part because it addresses the point as a whole.

The standard method is the correct one because most people use it, and that is not a logical fallacy.

Why? Because it is a matter of definition. The signs are used that way because that is how they are defined. There is nothing wrong with using a different definition, but if you do, then you have to explicitly say, if you do not specify what definition you are using then it is assumed that you are using the standard one.

That is true of every part of human communication. If you use a non-standard definition without clarification then you are being either obtuse or ignorant.

The original question does not clarify, therefore the standard is assumed. If you answer in a non-standard way, without clarification, then you are simply wrong.

Firstly, at no point did I change the definitions of the operators. This is why everyone understands the problem- pretty much everyone is mathematically literate and at least understand plus, minus and asterisk being used to indicate addition, subtraction and multiplication. What I am varying is the interpretation of the problem presented. This is standard for answering ambiguous mathematical problems- you state up-front your assumptions. I would give full marks to anyone who says 'assuming pedmas' or 'my calculator says'. Bonus marks for getting both.

I'm clearly not being ignorant here, but I am arguing on the behalf of the people at are. Lots of people struggle with math, or don't have the patience for it, certainly don't take their education that far with it. You are taking the standard convention, that exists for a very good reason amongst those who regularly use mathematics, and applying it to everyone. However, I think you'll find that while the Escapist may be somewhat eschewed towards more educated individuals, as is apparent in the poll, there is a significant number of individuals who think differently.

"Aha!' you may say, "argumentum ad populum", despite arguing in favour of that fallacy. Yes, it isn't always a fallacy. Certainly when it comes to democratic process, what is popular is considered correct. The same goes for social conventions and manners. The fallacy is that it cannot be used factually, for deductive reasoning- you cannot say 'this is mathematically correct because everyone believes these are the right rules'. The very word we use to describe it is convention. This implies that it is not the only method and that other answers are potentially valid solutions. We're not changing the rules of mathematics, just the conventions of the interpretation of expression.

So just because 30% of people got that answer, that doesn't make it correct. It's the fact that there exists a perfectly logical and consistent convention that gives that answer. Single-step execution mathematics is very easy to hold in the head and reflects what a simple pocket calculator and many cashier tills will do (i.e. add many items together, then multiply the entire amount by tax, without using brackets). There isn't any arbitrary and inconsistent addiction/application of brackets which makes the other ways to obtain different answers far less valid.

 

[Maze1125]

The standard method is the correct one because most people use it, and that is not a logical fallacy.

I think you're missing the point...

Yes, the standard (ie. correct) method of solving the problem will only lead to the answer of 14.
What makes the correct method correct is not the fact that the most people used it. It's because it follows the laws of Math.

Let's suppose that people continue to vote for '0' and gets more votes than '14'. By your logic, if and when '0' overtakes '14', the method that arrives at '0' becomes the new 'standard method', 'because most people use it'. Which, goes without saying, is wrong.

No it's not, that's right.
You've oversimplified the issue slightly, but if the majority of people who used Mathematics started using the operations in a different way, then that new way would be come the standard.

The laws of Maths are chosen by us, we define them. If humans as a whole agree that they should be different, then they will be different.

Stuff

And?
None of that changes the fact that if someone uses a non-standard definition without clarification, then that person is being either purposely obtuse or ignorant.

And yes, it is part of the definition of the operators themselves, the way brackets are defined give them priority over other operators, just as the way multiplication is defined gives it priority over addition. Not that it change my point in the slightest if it wasn't true, my point is that it is standard, not the specifics of where that standard is defined.

 

[madwarper]

but if the majority of people who used Mathematics started using the operations in a different way, then that new way would be come the standard.

The laws of Maths are chosen by us, we define them. If humans as a whole agree that they should be different, then they will be different.

No, that's wrong.

One plus one equals two because it is a universal truth, not because the people who say it equals two is greater than those who say it equals hand bananna.

Just because the majority believes one thing does not, nor has it ever, nor will it ever, make it correct.

At one time, the majority of people thought the world was flat. They were wrong.
At one time, the majority of people though Earth was the center of the universe. They were wrong.
Today, fortunately the people who said the answer to the given equation was '0' are in the minority. But, even if they ever became the majority, they would still be wrong.

 

[Maze1125]

but if the majority of people who used Mathematics started using the operations in a different way, then that new way would be come the standard.

The laws of Maths are chosen by us, we define them. If humans as a whole agree that they should be different, then they will be different.

No, that's wrong.

One plus one equals two because it is a universal truth, not because the people who say it equals two is greater than those who say it equals hand bananna.

Just because the majority believes one thing does not, nor has it ever, nor will it ever, make it correct.

At one time, the majority of people thought the world was flat. They were wrong.
At one time, the majority of people though Earth was the center of the universe. They were wrong.
Today, fortunately the people who said the answer to the given equation was '0' are in the minority. But, even if they ever became the majority, they would still be wrong.

1 + 1 = 2 because of the way we have defined the symbols 1, 2, + and =.
If I were to define those symbols in a different way, for example, define the plus symbol to mean the same the current multiplication symbol, then the result would be different. In that case, 1 + 1 = 1.

Would the underlying truths of the universe change because of our redefinition? No, of course not, but they way we wrote those truths would. By exactly the same point, our order of operations is just a convention of how it write things down, we could very well define it differently if we decided as a group to change it.

1 + 1 * 0 = 1 because we have defined the order that operations take place.
As has been said, simply taking the operations in order works fine, provided everyone knows that is what you are doing. You have to write equations down differently to get the same results, but it's a perfectly consistent system

 

[DanDanikov]

And?
None of that changes the fact that if someone uses a non-standard definition without clarification, then that person is being either purposely obtuse or ignorant.

Standard for who? Did you read my post? It's standard for mathematicians and physicists, not for Joe public who just has to tot up bills and apply taxes. Yes, it makes them ignorant to the wider world of maths, probably in the same way you're probably ignorant to how the scoring system works for Bridge. You don't need to know and being ignorant about that is in no way a bad thing, just in the same way their ignorance is not a bad thing. I take a fair amount of offence to the superior-than-thou attitude, but that is beside the point...

And yes, it is part of the definition of the operators themselves, the way brackets are defined give them priority over other operators, just as the way multiplication is defined gives it priority over addition. Not that it change my point in the slightest if it wasn't true, my point is that it is standard, not the specifics of where that standard is defined.

Let's switch places for a brief second, and I'll tell you exactly where you can attempt to attack my position. Firstly, you could argue that the problem is non-ambiguous. Secondly, you could argue that while the problem is ambiguous, the various interpretations presented are qualitatively inferior and therefore should be considered disregarded. Thirdly, you could argue that, while there are many equal interpretations, why one should be considered solely over the others.

The core of your argument seems to be that there is only one interpretation of mathematics, and in this you are somewhat correct. Subtraction, multiplication, division, they are all fixed. The problem isn't in the maths, it's in the communication of it. Brackets do not exist in maths, nor do they need to. There are alternate, valid notations, such as (reverse) polish notation, in which brackets are not needed to eliminate ambiguity. Also, because the underlaying maths won't change, you can happily translate between valid notations.

The problem doesn't make any effort to clarify which notation is in use, so we can safely say the problem is somewhat ambiguous. A full answer should state its assumptions, even if it's to what's considered standard, to prevent the ambiguity perpetuating into the answer, however the poll doesn't give that option, nor is there any way to give two or more answers (a variation on the false dilemma fallacy).

The single-execution approach hasn't been demonstrated to be qualitatively worse or incorrect, nor has there been anything other than a fallible appeal to popularity. What does seem to exist is a difference in interpretation (ironic). Mathematically, there is only one solution to a non-ambiguous statement. The problem we have here is resolving the statement to a point that is unambiguous and can be solved. Your arguments assume that pedmas is the only way to make that resolution and continue from there. My arguments are at a more fundamental level- that your assumption is merely an assumption and not considered solely to the exclusion of all others.

The baseline question seems to be whether or not pedmas should be the only interpretation of the question posed and how doing so would make all the other interpretations incorrect. Everything beyond that seems to be consistent in favour of the people who have been arguing for their respective positions.

 

[Maze1125]

And?
None of that changes the fact that if someone uses a non-standard definition without clarification, then that person is being either purposely obtuse or ignorant.

Standard for who? Did you read my post? It's standard for mathematicians and physicists, not for Joe public who just has to tot up bills and apply taxes. Yes, it makes them ignorant to the wider world of maths, probably in the same way you're probably ignorant to how the scoring system works for Bridge.You don't need to know and being ignorant about that is in no way a bad thing, just in the same way their ignorance is not a bad thing.

Ignorance itself isn't bad, ignorance about something you're trying to do is bad.
Everyone's ignorant about most things. As you guessed, I am mostly ignorant about the rules of Bridge, but if I were to try and play a game of Bridge, I wouldn't assume I did know the rules. I would make sure to look them up first, and if someone gave a quiz question on the rules of Bridge, I wouldn't try and answer it with any kind of certainty.

I have no problem with people being ignorant of Maths, I have a problem with people being ignorant about anything while being arrogant enough to assume they're not.

I take a fair amount of offence to the superior-than-thou attitude, but that is beside the point...

I'm sorry, what? What holier than thou attitude? I have simply been stating facts.
Anyone who uses a non-standard method without clarification is either obtuse or ignorant, with some level of unjustified arrogance on top. That is a fact. (possibly with a few minor exceptions, but that's beside the point)
Further, I think those are bad things, and I believe most other people do too. That is another fact.

I have a tendency to speak more formally around these things than most people, but that is not a holier than thou attitude, just how I present my arguments.

The mistake at hand is a very minor one. If I were in an actual situation, I wouldn't care at all.
But to claim it is not a mistake at all, is simply false. It is a mistake and it is born out of ignorance.

Now, while were on the subject of holier than thou attitudes, lets move on to the rest of your post...

Let's switch places for a brief second, and I'll tell you exactly where you can attempt to attack my position. Firstly, you could argue that the problem is non-ambiguous. Secondly, you could argue that while the problem is ambiguous, the various interpretations presented are qualitatively inferior and therefore should be considered disregarded. Thirdly, you could argue that, while there are many equal interpretations, why one should be considered solely over the others.

I'm sorry, what?
You're telling me how I'm allowed to argue? How unbelievably arrogant. The whole point is that I believe I know something you haven't thought of, and you think the same. That how argument and discussion occur.

But to not only think that, but to also claim you've thought of every conceivable possible retort I could use and you've worked out the only ones I'm allowed to use, and to do that right after accusing me of having a holier than thou attitude?

Wow... just wow...

The core of your argument seems to be that there is only one interpretation of mathematics,

No it isn't.

and in this you are somewhat correct. Subtraction, multiplication, division, they are all fixed.

No they're not. There's multiple different definitions for all of those. None of them are fixed, there are just standards.

The problem isn't in the maths, it's in the communication of it. Brackets do not exist in maths, nor do they need to. There are alternate, valid notations, such as (reverse) polish notation, in which brackets are not needed to eliminate ambiguity. Also, because the underlaying maths won't change, you can happily translate between valid notations.

And?

The problem doesn't make any effort to clarify which notation is in use, so we can safely say the problem is somewhat ambiguous.

No, when a problem doesn't clarify, then the standard is assumed. If someone told you "I was just drinking tea from my cup." you wouldn't think there was a reasonable possibility that they were drinking tea out of a groin protector, because that wouldn't be the standard and the person didn't clarify.

A full answer should state its assumptions, even if it's to what's considered standard, to prevent the ambiguity perpetuating into the answer, however the poll doesn't give that option, nor is there any way to give two or more answers (a variation on the false dilemma fallacy).

Yes, full answers should always state their assumptions, just like in real life everyone should clarify any statement that might be even slightly ambiguous.

But, as you also explain, that can't always be done, or can be done but simply isn't. For various reasons. And, in those cases, such as this poll, the standard is assumed.
That said, many people outright posted their answers as 0, where they very well could give their assumptions, yet still didn't.

The single-execution approach hasn't been demonstrated to be qualitatively worse or incorrect, nor has there been anything other than a fallible appeal to popularity. What does seem to exist is a difference in interpretation (ironic). Mathematically, there is only one solution to a non-ambiguous statement. The problem we have here is resolving the statement to a point that is unambiguous and can be solved.

The problem isn't the ambiguity, but your assumption that because ambiguity exists that both options are equal.
They are not.

Ambiguity exists in everything, nothing can ever be stated completely unambitiously. Even if you clearly define every single word in your statement, it can be argued that the words in the definitions haven't be defined themselves, leaving the definitions, and therefore the original statement, still ambiguous. And that can be done ad-infinitum.

Ambiguity always exists to some extent. Which is why we pick the standard when there isn't clarification. And when there is clarification, we pick the standard with-in that group. You've done exactly that. You've considered that maybe you could just take the operations in order, but you still assume the standard of going left to right when the operations could just as well be taken right to left in order. Once you reached the idea that going in order could be valid, you still assumed the standard with in that.

At some point you always have to go with the standard, you just arbitrarily do so at the second level, rather than the first.

Your arguments assume that pedmas is the only way to make that resolution and continue from there.

No it's not. My argument is that it is the most correct way with-in the Mathematics we have constructed as a race.

My arguments are at a more fundamental level- that your assumption is merely an assumption and not considered solely to the exclusion of all others.

So why do you exclude orderings that go in other ways? The left to right ordering is just an assumption, yet you exclude all the others, of which there are many.

The baseline question seems to be whether or not pedmas should be the only interpretation of the question posed and how doing so would make all the other interpretations incorrect.

No it isn't, answers that include both standard and non-standard methods and explain them both are inherently better than ones what just use one method. That doesn't change the fact that, given the question (like every question) has some level of ambiguity, the standard answer is a better one to give than a non-standard one.

 

[DanDanikov]

I'm sorry, what? What holier than thou attitude? I have simply been stating facts.

That comment was more directed at some other's people's comments on the problem, mainly the ones along the lines of 'oh, I can't believe how many people answered 0, people are so stupid, I weep for humanity', which is judgemental, smug and unbecoming behaviour. Categorising people who came up with a singular answer that doesn't agree with yours as either intentionally obtuse or ignorant does fall under that umbrella, but it was hardly the entire content of your post.

Anyone who uses a non-standard method without clarification is either obtuse or ignorant, with some level of unjustified arrogance on top. That is a fact. (possibly with a few minor exceptions, but that's beside the point)
Further, I think those are bad things, and I believe most other people do too. That is another fact.

It really isn't a fact, it's a judgement, or rather, an opinion. You are entitled to your opinion, as I am entitled to my opinion of that opinion, but there's not much point arguing over opinions. If you want to be pedantic, that you hold such opinions is factual, but entirely irrelevant, because what can we derive from such opinions?

The mistake at hand is a very minor one. If I were in an actual situation, I wouldn't care at all.
But to claim it is not a mistake at all, is simply false. It is a mistake and it is born out of ignorance.

It's only a mistake within the context of applying pedmas. If you're not applying pedmas, it isn't necessarily a mistake (unless you want to argue that not applying pedmas is a mistake in itself).

You're telling me how I'm allowed to argue? How unbelievably arrogant. The whole point is that I believe I know something you haven't thought of, and you think the same. That how argument and discussion occur.

But to not only think that, but to also claim you've thought of every conceivable possible retort I could use and you've worked out the only ones I'm allowed to use, and to do that right after accusing me of having a holier than thou attitude?

Actually, what I was doing was attempting to see the whole problem, not just my perspective of it. I made some assertions as to where I personally thought the weak points were, how I'd refuted them, and thus decided my position was correct. The idea is that you can then go on to point out where we may agree, disagree, or that I've missed something. Ultimately, we must either find common ground that leads to an agreed conclusion, or basic principles that we cannot agree on.

No, when a problem doesn't clarify, then the standard is assumed. If someone told you "I was just drinking tea from my cup." you wouldn't think there was a reasonable possibility that they were drinking tea out of a groin protector, because that wouldn't be the standard and the person didn't clarify.

Actually, context can have a huge effect on that. If a cricketer were to say that in a comedic context, it'd potentially be very funny. Context is very important, and different standards exist in different contexts. Perhaps I should reword my (tentative) assertion that the core of your argument (seems to be) that there is only one standard and universal interpretation of mathematics that should only ever be used by default in the absence of qualification..

I don't disagree that pedmas is by far the best assumption to make. I just disagree that it's the only assumption to make and thus to consider all other answers wrong. The ideal answer to this is to state which answers (answers, plural) may be considered correct based on which assumptions, purely because there is no context or clarification.

The problem isn't the ambiguity, but your assumption that because ambiguity exists that both options are equal.
They are not.

Nice to see that, despite thinking my earlier statement arrogant, it at least drove the discussion forward- we agree that it is ambiguous, but we disagree that the options are equal. Now we're getting somewhere.

Ambiguity exists in everything, nothing can ever be stated completely unambitiously. Even if you clearly define every single word in your statement, it can be argued that the words in the definitions haven't be defined themselves, leaving the definitions, and therefore the original statement, still ambiguous. And that can be done ad-infinitum.

I almost retract my previous statement- you're verging on what Stephen Law terms 'going nuclear' where you can argue that all arguments are based on induction, which is ultimately circular, or unfounded. Thus, reason cannot be used and the argument ends.

Ambiguity always exists to some extent. Which is why we pick the standard when there isn't clarification. And when there is clarification, we pick the standard with-in that group. You've done exactly that. You've considered that maybe you could just take the operations in order, but you still assume the standard of going left to right when the operations could just as well be taken right to left in order. Once you reached the idea that going in order could be valid, you still assumed the standard with in that.

So why do you exclude orderings that go in other ways? The left to right ordering is just an assumption, yet you exclude all the others, of which there are many.

Actually, the best way to deal with ambiguity is to eliminate it with further information. Standards are useful as they allow people to stop thinking about variation. Standards are dangerous for the exact same reason. Also, I've actually worked backwards from the most common answers being 14 and 0. The fact that both are popular suggests they are based on reasonable, logical and consistent approaches to solving the problem. The fact that there exists two popular approaches suggests that those variations have arisen out of different contexts that give rise to different standards. I may consider many other approaches to be 'valid', but I'd be safe to infer that most people in future will use one of those two approaches, and answers outside of those two are likely (but not certain) to be mistakes within either one or the other approach.

At some point you always have to go with the standard, you just arbitrarily do so at the second level, rather than the first.

My argument is that it is the most correct way with-in the Mathematics we have constructed as a race.

Again, standard for who? Sounding like a broken record here, but standards aren't universal. Kids doing physics don't know about vectors. Highschool students don't have to worry about general or special relativity when working with gravity. Sure, vectors or Einstein's physics are more correct, as is pedmas, but that doesn't mean that they are used in every context and become the de facto standard- it's very much contextual. Not everyone has been educated to your mathematical level and while they may know less maths than you, it doesn't make their maths wrong.

Also, I'd disagree that pedmas is the best/most correct for Mathematics, but it's good for the level of maths that you seem to consider 'standard'.

Answers that include both standard and non-standard methods and explain them both are inherently better than ones what just use one method.

We definitely agree there, however not everyone is going to bother voting in a poll and commenting on it as well, and not everyone is going to be as aware of that ambiguity. I also agree that the pedmas approach is a higher level approach, which if forced to make a singular answer, would be grounds for considering that answer to be better. However, better answers don't make the other answers wrong, and saying both answers are technically correct shows more understanding than selecting one or the other.

I'm quote open to you stating what you think I'm thinking, and where you think I've gone wrong. Or maybe you want to try the 'other viewpoint' approach and share where you think your weaknesses were and how your justified your perspective. I'd be very interested to hear what you think our common ground is, at least.

 

[wootsniper]

1) 1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+1*0 = ?
2) 1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+0 = ?
3) 10-1+1+1+1+1+1+0 = ?
4) 10-1+5+0 = ?
5) 9+5 = 14

cuz the 1*0 gets priority and the rest is to be solved one by one from left to right because plus and minus have equal priority.

Someone please tell me if I'm wrong,

(AND DON'T TELL ME THAT I WAS "IMAGINING" FUCKING BRACKETS)


If you do it wrong step 4 might be 10-6+0 = 4

 

[wootsniper]

The answer is minus infinity.
(1+1+1+1+1+1+1+1+1+1)-(1+1+1+1+1+1+(1/0))
=10-(6+infinity)
=10-infinity
=-infinity
If the end was 1*0= then the answer would be 4 as adding brackets the sum equates to
(1+1+1+1+1+1+1+1+1+1)-(1+1+1+1+1+1+(1*0))
=10-(6+0)
=4

you confused (X)-1+1+1+1+1+1 for (X)-6, instead of (X)-1+5=4