Open-Ended Math Questions?

[Soapy Sam]

But if you take a pen and a piece of paper and divite 1 by 3, it should be obvious that the result involves an infinite strings of 3s after the comma. You can't write it down to the end, but you can see that there is no other way the number could develop. There will be more 3s and nothing else.

Rasmus, I'm afraid this is far from obvious to me, and if I have learned anything from reading about relativity, quantum mechanics and many other aspects of reality it is that things which do seem obvious, when in unfamiliar territory, are often wrong. And like you, I consider infinity to be unfamiliar territory. The human mind did not evolve around infinities and I suspect may not have any intuitive grasp of their properties, supposing them to exist at all.

Likewise, you cannot complete on a piece of paper all the steps it would take to figure out what 0.333... and 0.333... and 0.333... is. But you can easuly figure out that the result will be 0.999... no matter how far you go. You can see that if you were to write the number down that way it would require an infinite string of 9s.

And if 1/3 + 1/3 +1/3 = 1, then so must 0.999...

Rasmus.

It is precisely because neither I nor (so far as I have heard) anyone else can do it that I say it perhaps cannot be done even in theory and is , accordingly, either paradoxical or meaningless.

 

[DeviousB]

I think you meant this link here

Thanks for that. I don't know how the ")" got on the end of my link, given that I just cut&pasted it.

And, no, it's not axiomatic. Just as a simple example (from that page)

I was thinking of the bit...

Construction by decimal expansions We can take the infinite decimal expansion to be the definition of a real number, considering expansions like 0.9999... and 1.0000... to be equivalent, and define the arithmetical operations formally.

 

[69dodge]

Anyway, the solution should be x = -0.5 +/- sqrt(3)/2i.

Yes.

Just to clarify for others: it's sqrt(3)/2 i, not sqrt(3) / 2i.

Although now that I think about it, it doesn't really matter in this case, because it would just turn the "+/-" into "-/+".

And the error I think works out to the same spot. x + 1/x != -1.

Sorry to do this again, but...

?

Those numbers do satisfy x + 1/x = -1.

 

[69dodge]

Rasmus, I'm afraid this is far from obvious to me

If you divide 1 by 3 using long division, at each step of the process you are faced with precisely the same situation, namely that the next digit in the answer should be the (largest whole) number of times that 3 goes into 10. If the answer was 3 the last time, how could it fail to be 3 this time as well?

And each of the infinitely many times is a this time of exactly this type, whose last time gave the answer 3; so it too must give the answer 3.

So all the digits are 3's.

You do not find this argument convincing?

 

[69dodge]

I think we have to agree on what is meant by "equals" in your question.

If you mean: Are " 1/2" and "0.5" the same?
Then the answer is clearly "no". A glance is sufficient to distinguish them.
That's the symbolism question.

If what you mean is " Does the operation 'one divided by two' yield the number represented by the symbol '0.5' , then the answer is "yes".

I think we pretty much agree here, although I would phrase it differently. The question isn't what "equals" means---it means: really, really, exactly the same. No, no, even the samer than that. The question rather is, what do I mean when I write stuff with quote marks around it, and what do I mean when I write it without any quotes?

When I write stuff with quotes around it, I'm referring to the sequence of letters/digits/symbols within the quotes; when I write stuff without quotes around it, the stuff is supposed to be the name of something, or a description of something, and I'm referring to whatever it names or describes.

For example, if I write 'a red house', I'm talking about a physical building, but if I write 'a red "house"', I'm talking about something like this:

house​

So the idea is that "1/2" and "0.5" are two different names for the same number. And "1/4" and "0.25" are both names for some other number. Etc.

What these numbers are exactly, which have names like "0.5" and "0.25", is not an easy question to answer. Possibly, the most philosophically defensible position is that actually there aren't any such things. But it's convenient to pretend that we're talking about something, rather than that we're just talking. So that's what people do.

Until some down-to-earth guy such as yourself comes along and starts asking hard questions.

Actually, the modern approach is to define numbers in terms of set theory. But that just pushes the question down a level; it doesn't get rid of it. We may have a satisfactory definition of numbers---they're certain sets---but now we have to answer the question, what are sets? Do sets really exist, whatever that means? I know of no conclusive answer. Platonists say that sets really exist; formalists say that all that really exists are the statements we make, which apparently are about sets but which really aren't about anything, because there aren't any such things as sets for them to be about.

In this example the distinction is trivial. But what about this one?
Does 1/3 = 0.33?

The practical answer is "It depends.Are we talking currency , or what?"
But that's a question about quantity.

I'm not sure what you mean by "quantity".

I don't think it's ever right to say that 1/3 equals 0.33. The definition of 1/3 is that three of them together make 1. But three times 0.33 isn't 1; it's 0.99.

If you're thinking about figuring tax on a dollar, or something like that, the rule isn't in fact that the tax is 1/3 of the amount. Rather, the rule is something like, "the tax is 1/3 of the amount, rounded to the nearest penny; but if it's exactly halfway between two pennies, then round to the one that's even".

If we are talking pure numbers, detached from the real world, the answer , surely , is "No- 1/3 is NOT the same as 0.3" or .33 or .333333

If now we simply define 1/3 as being equal to (.333...) well, as AS says, you can't argue with an axiom in mathematics.
But you can and must in the real world. The supposition that spirit exists is not one I am willing to admit at the start of a discussion on life after death. It's what is to be proved. We must question assumptions. We must look for paradox, or for evidence that supports or contradicts the assumption.

Yes, absolutely. It's good to ask questions.

In some sense, we do, as you say, simply define 1/3 as being equal to 0.333... . But in another sense, this definition is not the least bit arbitrary. We really don't have any choice in the matter. If "0.333..." is to represent any number at all, it has got to represent 1/3. And if 1/3 is to have any decimal representation at all, its decimal representation has got to be "0.333...".

Suppose you take a metrestick, and make a mark exactly one third of the way from one end. (Yes, I know it would be much easier if you used a yardstick. That's not the point, ok? ) The mark will be between 333 mm and 334 mm from the end. That is, between 0.333 m and 0.334 m. So, the exact distance in meters has to be 0.333something. Now, regardless of what the something is, it can't make the number less than 0.333 nor can it make the number greater than 0.334, right? Even if the something goes on forever, so what? The digits way out there represent only tiny, tiny distances along the metrestick; and the farther out they are, the tinier are the distances that they represent. So there's no need to worry greatly about the fact that there might be infinitely many of them. They won't add up to much, even all infinitely many of them together, because they get ever and ever tinier.

In fact, they will add up to ... drumroll, please ... exactly 1/3. But we haven't gotten to that yet.

(to be continued. I'm getting tired.)

If, when counting beans, I assign an uncountable number of integers to each bean , my total count will be meaningless. Yet this is exactly what infinities do.

[...]

(As opposed to very small numbers, or simply "uncountable" numbers). Why must this be?

If we redefine an infinity as a number which is simply not countable, then there is no actual requirement for it to be a big number.

(But in the meantime, can you clarify what you mean by "uncountable"? I have no idea what sort of thing you're thinking of. The terms "countable" and "uncountable" have specific technical meanings in set theory, but you don't appear to be talking about those. [Set theory not only deals with infinity, it deals with many different sizes of infinity---infinitely many, in fact. Some of the smaller ones are called "countable". The bigger ones are all called "uncountable".])

Sorry if all this seems like / is total nonsense. It may well be. [...] I hope this does not seem too stupid.

Hey, don't apologise. People had trouble with infinity for thousands of years. Cantor only figured it out like 100 years ago. And that was just the basics. More stuff has been done even more recently than that. So it's not so easy.

And your question-
what's 0.333333... + 0.989898... ? You will appreciate, given my beliefs, that it would be sacreligious to attempt an answer. Indeed I demand you apologise for asking it. I propose to riot in the street and burn you in effigy.

Right. I'll make you a deal. I'll apologise for asking it if you answer it.

 

[ReFLeX]

b o r i n g.

Sorry, I don't know about anybody else, but if I'm not interested in a thread I close it, not post in it.

 

[ReFLeX]

Re: the sequences starting with only two numbers (i.e. 2, 4, what's next?) that can make for a pretty good open-ended question. Start with any two numbers and show that three different numbers could follow, with three different formulas. For more of a challenge, find one that has infinite possible next numbers.

 

[DeviousB]

Re: the sequences starting with only two numbers (i.e. 2, 4, what's next?) that can make for a pretty good open-ended question. Start with any two numbers and show that three different numbers could follow, with three different formulas. For more of a challenge, find one that has infinite possible next numbers.

Um, they all do.

 

[Soapy Sam]

69Dodge-

First- Thanks for your tolerance. It is appreciated.

An example of what I mean by "quantity" would be "Three cows". Cows are the object of the quantity, three the magnitude of it.

My nasty suspicion is that when we abstract "number" from the concept "magnitude of a quantity" and simply discuss "three" instead of "three cows", we actually lose more than cows. We lose a tangible test of reality.
We start assuming things which may be right or wrong but are to some extent untestable.

Half of three cows, any way we look at it, is a bloody mess. Half of three is a neat "1.5" Something has been lost in the abstraction. I make no pretense of knowing what, but it sometimes keeps me awake at nights.

Because we can multiply four yards by five yards and get 20 square yards may not imply that multiplying 4 by 5 should give 20. Everyone thinks it does - and it certainly seems to. But I wonder.

In the case of 1/3 , I can think of no number which will appear in the answer except three, no matter how far protracted, but because I see no alternative does not mean that none exists. I don't know what happens in an infinite sequence. I don't think anybody does. We assume we know and we may be right.

Being no mathematician, I have the luxury of admitting my ignorance and just sitting there, thumb in mouth. I remain unconvinced, while admitting I have no better alternative to offer.

When I said "1/3=.33", I meant purely in the sense of rounding tolerances as in a spreadsheet, where currency calculation is generally (displayed)to 2 decimals- and division is a comparative rarity.

The metrestick example-
I agree absolutely that the measurement converges on a result between 333mm and 334mm This seems to imply that the nth value in the convergent series is immeasurably small;- but I would argue that it cannot be if there is a Planck length. It is either measurable, or it is not there. If the universe has a quantum size limit- a grain- there can be no infinitesimal values in reality. (Measurement tolerance would , of course, fade out many orders of magnitude higher, but this is a gedankenexperiment right?)

(This is essentially the "half a cow" effect, writ small- we are safe so long as we limit our imagination to number, but quantity demands that we meet the requirements of physics as well).
Is there, meaningfully, a point exactly 1/3 along the stick? Again, I don't know. Is there, meaningfully such a number as 0.333...? We see no reason why not because we have discarded the physical requirements. But is that legitimate?

"Uncountable" ? Define this? That'll larn me.
Can a number exist which is uncountable, yet has a value? An infinite number would appear to be uncountable- is that not the whole point? If it's countable, then there exist smaller and larger numbers, also countable, so it cannot be infinite. There is a linguistic paradox here. If there is a linguistic definition of infinity that does not involve similar paradox, could you let me know what it is please?

I propose uncountability as the definitive characteristic of infinity because it does seem impossible to count an infinity and because it removes the requirement for infinities to be big. For example, the additive total of the "9" s in the series "0.999..." does not add up to a big number, while the number of "9"s (The magnitude of the quantity of nines) remains itself unlimited. (I have been surprised by people saying this series does not involve an infinity, when it clearly does. It is simply not a big infinity. I think infinities do not need to be big, though their expressions may be unlimited.)


In answer to your puzzle, I'm afraid all I can do is add the two numbers to the number of significant places shown , which (mental arithmetic here) gives 1.323231
I presume correctly this would repeat(... 323232323... )until one chose to stop, but if the two numbers are themselves meaningless (which remains my supposition), I doubt the answer has meaning either. It is as if, from DRKitten's example, I added "Oxford" to "Buick Century" to obtain (Oxford & Buick Century). Except in terms of string handling, it does not seem meaningful. Uncountable, too!

 

[drkitten]

An example of what I mean by "quantity" would be "Three cows". Cows are the object of the quantity, three the magnitude of it.

My nasty suspicion is that when we abstract "number" from the concept "magnitude of a quantity" and simply discuss "three" instead of "three cows", we actually lose more than cows. We lose a tangible test of reality.
We start assuming things which may be right or wrong but are to some extent untestable.

Half of three cows, any way we look at it, is a bloody mess. Half of three is a neat "1.5" Something has been lost in the abstraction. I make no pretense of knowing what, but it sometimes keeps me awake at nights.

Well, when you abstract "three" from "three cows," you lose something. You lose the cows. But that shouldn't keep you awake at night.

What you're not seeing -- and again, this isn't surprising, since to understand this properly can require some high-level mathematics -- is that there are actually several different number systems out there. Most elementary school children, for example, are familar with "whole numbers" and "fractions," and by the time you get to high school you probably know about "integers" and "real numbers."

But everyone is famililar with clocks. And those are a number system unto themselves as well. What's five hours before 2a.m.? Not -3 a.m.

So when you try to manipulate "numbers" in a realistic way, you need to pick your system correctly. Cows, as you pointed out, just don't come in fractions -- not normally, in any case. Trying to "divide" an odd number of cows by two isn't a legitimate operation. That's not a problem of mathematics, but of the individual mathematician who didn't pick his tool properly. There's a perfectly sensible number system out there that you can use to describe cows and other things that don't come in fractions -- but it doesn't give you enough power to describe things that do come in fractions, such as gallons and half-gallons of milk.

Because we can multiply four yards by five yards and get 20 square yards may not imply that multiplying 4 by 5 should give 20.

Of course not. Not always. If it's midnight, and I watch five four-hour movies, it's not twenty o'clock. It's 8pm. So in this case, 4*5 = 8. (The formal term for this kind of number system is "modular arithmetic.")

Everyone thinks it does - and it certainly seems to. But I wonder.

In the case of 1/3 , I can think of no number which will appear in the answer except three, no matter how far protracted, but because I see no alternative does not mean that none exists.

Well, this is where "proof" comes in. 69dodge gave you a proof based upon the division process. We know it won't come in in the first digit, because we can do the math. But we also know that the math for the second digit, and the third, and so on, endlessly, will be identical. Divide 10 by 3 and get 3, remainder 1 -- drop another 0 to get a 10 (to divide by 3).

I don't know what happens in an infinite sequence.

The same thing that happens in a finite sequence, except it takes longer.

I don't think anybody does.

I'm sorry -- I do know.

You're thinking, again, of "infinity" as a kind of number. It's not. At this level, its a description of a process -- a process that need not end. But at each point in the process, it's identical to our normal finite processes, so our intuitions about the intermediate stages are still legitimate. Things may break down when we try to extrapolate to a hypothetical end state -- but that's because, by definition, there is no "end state" for the process.

"Uncountable" ? Define this? That'll larn me.
Can a number exist which is uncountable, yet has a value? An infinite number would appear to be uncountable- is that not the whole point? If it's countable, then there exist smaller and larger numbers, also countable, so it cannot be infinite. There is a linguistic paradox here. If there is a linguistic definition of infinity that does not involve similar paradox, could you let me know what it is please?

"Uncountable," in set theory, is a term of art. A better term -- but mathematicians don't always have the luxury of picking the best possible term for a concept -- would be "enumerable."

A "countable'" infinity is an infinite process that can be carried out as a series of discrete, countable, steps. For example, I can "count" the positive integers as follows : 1, 2, 3, 4, .... Although I can never get to the end, I do know that any specific positive integer will be in that sequence somewhere, and that no integer will appear more than once. (In technical terms, this is a 1:1 and onto mapping.) The positive integers are thus a "countably infinite" set.

Similarly, the primes are a countable infinite set. I count them as follows : 2, 3, 5, 7, 11,... I will get every prime, and I won't double count any of them. So the primes are also a countably infinite set.

The number of real numbers, or the number of functions, are not countable. There's no way to set them up so that I can enumerate them one by one and make sure of getting all of them. (Again, this is provable, but the proof details might be confusing. If you want to read the proof, it's "Cantor's diagonalization.")

I propose uncountability as the definitive characteristic of infinity because it does seem impossible to count an infinity and because it removes the requirement for infinities to be big.

In your sense of "uncountable" -- meaning, a process that cannot be continued to an end -- you're more or less right. If the process by which you get to something does not end, that something is "infinite."

For example, the additive total of the "9" s in the series "0.999..." does not add up to a big number, while the number of "9"s (The magnitude of the quantity of nines) remains itself unlimited. (I have been surprised by people saying this series does not involve an infinity, when it clearly does. It is simply not a big infinity. I think infinities do not need to be big, though their expressions may be unlimited.)

You're not understanding. The magnitude 0.99999.... is not infinite, nor does it involve an infinity to calculate that total. The expression "0.999...." is of course infinite. But that's back to your point about magnitude vs. quantity (which I admit I didn't fully understand -- your terminology is confusing). The magnitude of 0.999... can be determined fully using a limit process without using any infinite processes.

Basically, what I can do is I can prove that the result of a particular finite process lets me get as close as I like to the actual answer. This means that if I need accuracy to within 1%, I only need to use the first (e.g.) three digits, since the remaining unbounded sequence cannot change the value by more than 1%. If I can prove that for any x% accuracy, I need only look at the first y digits (y might be x+1, or 2x, or something like that), then I can calculate the value of the infinite sequence exactly.

 

[ReFLeX]

Um, they all do.

Really, can you show me that?

 

[GreedyAlgorithm]

Really, can you show me that?

I can show you. Suppose you have a sequence of terms a1, a2, ... an. Then those terms could be given by the formula
[latex]$$\lfloor b_1+b_2x+b_3x^2+...+b_{n+1}x^{n} \rfloor$$[/latex]
where the coefficients satisfy
[latex]$$\left( \begin{array}{ccccc}
1 & x & x^2 & x^3 & . \\
1 & x & x^2 & x^3 & . \\
1 & x & x^2 & x^3 & . \\
1 & x & x^2 & x^3 & . \\
. & . & . & . & . \end{array} \right) \left( \begin{array}{c}
b_1 \\
b_2 \\
b_3 \\
b_4 \\
. \end{array} \right) = \left( \begin{array}{c}
a_1 \\
a_2 \\
a_3 \\
a_4 \\
. \\
k \end{array} \right)$$[/latex]
Since this works for any integer k, then any integer k could be the next in the sequence, for any given starting sequence.

 

[drkitten]

Really, can you show me that?

Um, yeah. it's pretty easy, actually.

Pick two value, A, and B. Since any three points define a parabola, I can pick my own value z.

Let P be the parabola going through (1,A), (2,B), and (3,z).

I then let the sequence A, B, z, w, ... be the sequence generated by the y-coordinates of the parabola at points 1, 2, 3, 4, ...

In fact, I could pick two arbitrary values and use a cubic polynomial. Or, in fact, I could let you pick N values, pick M values myself, and then use an N+Mth degree polynomial.

 

[Almo]

There are definately open ended Math problems. I believe you are refering to Arithmetic problems. Big difference.

Definately all "Whats the next number in this series' questions are open-ended.

There are no less than 4760 clearly defined mathematical sequences that have '1, 2, 3, 4' within them.. and clearly there are a lot more.

To list a few:

*list*

need I go on? extremely open ended.

But are these really useful questions? What do they teach? My contention is most of the useful questions are not open-ended. Like nosing through really hard "show that (ugly expression = other equally ugly expression)" type problems is where you learn how to plow through steps and get the right answer. Proofs have multiple ways to go about them, but you still need the right answer at the end. These teach the students to organize their thoughts on paper in the pursuit of a goal. Goals in mathematics are often well-defined, but the way to them is what's mysterious.

​

In a vain attempt to make math "accessible," I find that the quality of instruction goes down. My geometry teacher in high school was a tough bastard who made sure we learned formal logic skills. Those skills have served me well all the way through 4 years of grad school in physics and many subsequent years of computer programming and game design. The geometry teacher who succeeded him brought in these warm-fuzzy teaching tactics. I saw what those students were doing, and it was useless garbage. Sure, their grades probably went up, and they were probably less intimidated. But they didn't learn spit. Learning is hard work, and softening math with open-ended questions isn't going to help anyone. What is really important, in my opinion, is to find a way to help students understand why math is relevant.

As an example, one problem I had in alegbra was that I didn't like to show all my steps. It took more time to write the steps than to solve the problem in my head. What they didn't tell me was that developing the habit of writing all the steps would help once the problems were so hard I wouldn't be able to do them in my head anymore. And that it would also help me learn to organize my thoughts on paper; this skill is terribly important to learn, and math is one subject that can help people learn it.

 

[drkitten]

But are these really useful questions? What do they teach? My contention is most of the useful questions are not open-ended. [/QUTOE]

Actually, I'd argue just the opposite. Most useful questions are open-ended, and they're open-ended in precisely the way that the series questions are. We have some data, but not enough of it, and we're trying to predict what "the next element" in the sequence will be.

Two months ago, XYZ corp sold at $15/share. Last month, it sold at $10. Today, it's selling at $7. What number extends the sequence 15, 10, 7, ... --- and should I buy, sell, or hold?

Yesterday, the patient's temperature was 38. This morning, it was 39. RIght now, it's 38. Is the patient getting better or worse? Do we continue with the current round of medicine or change drugs?

The global average temperature is up about 0.6 degrees over the past century. Will this trend continue, or will temperatures revert to their previous (19th century) levels?

Most of business planning -- or any other kind of planning, for that matter -- is trying to find a plausible extension of previous trends. As any modeller will tell you, you can extend a trend to anything ("Don't stand where the comet is assumed to hit oil.") What these simple sequence problems teach you to do is to recognized patterns, to extend them, and eventually, to learn how to select among different competing pattern-extensions.

As rockoon pointed out, there are at least 4000 well-defined sequences including 1,2,3,4,... But it's much more likely when you're dealing with a simple accumulative process to be a simple arithmetic sequence than the set of 3-smooth or Niven numbers. On the other hand, if we're dealing with a process known to be combinatoric, then maybe we're dealing with something like the bead necklace question.

And part of mathematics education is to both give you the sequences (so that you've got a lot of shots in your locker) as well as the tools to selecte the appropriate sequence when needed.

 

[gnome]

If I might toss in a point...

The algebraic proofs I have seen may not be rigorous, formal proofs. The purpose they serve (IMO) is to convince someone who doesn't trust that .99999... = 1, and doesn't wish to examine the lengthy formal proofs needed.

It may not be formal, but it should be quite convincing.

My favorite:

x=0.9999999...=0+.9 + .09 + .009 + ...
10x=9.999999...=9 + .9 + .09 + .009 + ...
10x-x=(9-0) + (.9-.9) + (.09-.09) + ...
9x=9+0+0+0+0+0....
9x=9
x=1

Anyone that isn't convinced by that (because they wish to bring in more rigor) has no excuse but to learn and examine the formal proofs. At that point it's beyond lay discussion.

 

[Marquis de Carabas]

If I might toss in a point...

The algebraic proofs I have seen may not be rigorous, formal proofs. The purpose they serve (IMO) is to convince someone who doesn't trust that .99999... = 1, and doesn't wish to examine the lengthy formal proofs needed.

The argument I've had the most success converting the wayward with is not a formal proof, or really a proof of any kind, but a question:

For any two real numbers a and b, there is a third number x which is the difference between them. For the numbers 0.999... and 1, then, what is x?

This usually leads to the answer 0.000...1, but once the absurdity of that particular construction is explained, I have found that most people see reason. Most, not all.

 

[ReFLeX]

I can show you. Suppose you have a sequence of terms a1, a2, ... an. Then those terms could be given by the formula
[latex]$$\lfloor b_1+b_2x+b_3x^2+...+b_{n+1}x^{n} \rfloor$$[/latex]
where the coefficients satisfy
[latex]$$\left( \begin{array}{ccccc}
1 & x & x^2 & x^3 & . \\
1 & x & x^2 & x^3 & . \\
1 & x & x^2 & x^3 & . \\
1 & x & x^2 & x^3 & . \\
. & . & . & . & . \end{array} \right) \left( \begin{array}{c}
b_1 \\
b_2 \\
b_3 \\
b_4 \\
. \end{array} \right) = \left( \begin{array}{c}
a_1 \\
a_2 \\
a_3 \\
a_4 \\
. \\
k \end{array} \right)$$[/latex]
Since this works for any integer k, then any integer k could be the next in the sequence, for any given starting sequence.

Ok, that might be the smart way to do it, but what about as a kid working it out with pencil and paper? I mean, can you on your own arbitrarily choose some numbers and generate three formulas for three different sequences? It took me half an hour to get two answers with my Grade 12 level math. Once using 0 and 1, and then 1 and 2. And if a kid comes up with the aforementioned "easy solutions", well that's phenomenal, and goes to show the open-endedness of the question. I think it's one of the best such problems proposed so far.

 

[Almo]

Two months ago, XYZ corp sold at $15/share. Last month, it sold at $10. Today, it's selling at $7. What number extends the sequence 15, 10, 7, ... --- and should I buy, sell, or hold?

This is not a question that you use mathematics to solve. If math could solve the stock market, there'd be some very rich mathematicians by now. Some basic math is involved in assessing the value of the choices, but the final decision comes down to careful analysis of many, many other factors, some of which are mathematical, some of which are not.

Learning to solve these sorts of questions is not the provence of a math class.

 

[drkitten]

This is not a question that you use mathematics to solve.

The hell it isn't.

If math could solve the stock market, there'd be some very rich mathematicians by now.

And there are.

Have you ever heard of the Black-Scholes model for derivative pricing? Black was a math Ph.D. from Harvard, taught for a while at MIT (I think), and eventually joined Goldman Sachs. And a Nobel Laureate.

Some basic math is involved in assessing the value of the choices,

And often some really advanced math, too.

I believe that more mathematicians are employed on Wall Street than in academia.