# B Looking for internet famous math prob on dist law.

#### houlahound

A few years ago it was a big thing where high school basic math definition stumped a lot of pro mathematicians.

The prob from memory involved order of operations. Could be wrong but I think it was getting the correct answer to;

a(b+c) for specific values of a,b,c. All integers and no tricks.

Some maths profs argued for their answer some changed but the only answer was it was not a well defined question. Few conceded the other guy was right, or how they were wrong.

Sorry I can't define the actual problem but it started a math educator war. Hope my vague definition triggers someone's memory.

#### houlahound

OK pretty sure this is the problem although the numbers are irrelevant.

6÷2(2+1)

What is the solution to 6÷2(1+2)=?: Professor of …:

#### micromass

I'm gonna doubt that this stumped any pro mathematician

#### micromass

May well be urban myth but apparently different calculator brands give different answers although I have not tested that assertion.
That is correct. That means that the calculators were programmed incorrectly. They were programmed incorrectly because when typical students type in 6÷2(1+2) they often mean the incorrect thing.

The PEMDAs do work and they do give a clear answer.

#### micromass

Position 2 is crap. Find me some mathbooks that define "implied multiplication". You won't find it. I have never even heard of "implied multiplication" before this problem came around. Go ahead, search in Rudin, Bloch, Landau, or any other math book that rigorously defines numbers and their operations. Nowhere will you see that "juxtaposition" in any way behaves as position 2 tells us.

#### houlahound

Still a good discussion topic for students tho.

#### pwsnafu

The problem stems from some people assume that
1. $a/bc$ is equal to $\frac{a}{bc}$ instead of $\frac{ac}{b}$, or
2. people who think "implicit multiplication" (i.e. mathematical dot) and "explicit multiplication" (i.e. times symbol) are different. This is nonsense, there is only one multiplication of real numbers.

#### micromass

Still a good discussion topic for students tho.
Not really. It's completely irrelevant to mathematics. It's a stupid convention. Besides, nobody uses ÷ to denote division anymore.

#### micromass

If you want a good discussion topic for students, then talk to them about the value of $0^0$. For this, both sides actually do have a good point.

#### pwsnafu

If you want a good discussion topic for students, then talk to them about the value of $0^0$. For this, both sides actually do have a good point.
There is also "Is zero a natural number?"

#### micromass

There is also "Is zero a natural number?"
Or $0\cdot \infty$, where the convention that it equals 0 sometimes makes a lot of things easier in some parts of math (measure theory).

#### houlahound

Great discussion topics, will do some work. Thanks.

2^2^2^2^2^2^2^2^2...etc

Sorry can't make it nested.

#### micromass

Great discussion topics, will do some work. Thanks.

2^2^2^2^2^2^2^2^2...etc

Sorry can't make it nested.
Or $\sqrt{2\sqrt{2\sqrt{2\sqrt{2\sqrt{....}}}}}$.

Or the truly amazing

$$\pi = \frac{4}{1+ \frac{1^2}{3 + \frac{2^2}{5+\frac{3^2}{...}}}}$$

#### micromass

And if you really want to upset the class:

#### micromass

Interesting until I got to this and my heart sank;

"The Lambert W relation cannot be expressed in terms of elementary functions"
That doesn't mean anything. Why do you think the sine function is any more natural than the Lambert W function? We only know a limited number of exact values for the sine function too.

#### houlahound

On a simple note the correct answer to this finite problem?

2^2^2^2^2^2^2^2^2

#### houlahound

I think the sine function is more natural cos it is more natural;

tide comes in, tide goes out therfore sine.

That doesn't mean anything. Why do you think the sine function is any more natural than the Lambert W function? We only know a limited number of exact values for the sine function too.

#### micromass

On a simple note the correct answer to this finite problem?

2^2^2^2^2^2^2^2^2
Like expected, my computer gave an overflow error.

#### micromass

I think the sine function is more natural cos it is more natural;

tide comes in, tide goes out therfore sine.
So it's only natural because you can find an application of it in nature?

#### houlahound

By definition of the word natural your comment is trivial.

#### micromass

OK. But then (all from wiki)

The Lambert W function has been recently (2013) shown to be the optimal solution for the required magnetic field of a Zeeman slower
The Lambert W function was employed in the field of Neuroimaging for linking cerebral blood flow and oxygen consumption changes within a brain voxel, to the corresponding Blood Oxygenation Level Dependent (BOLD) signal.
The Lambert W function was employed in the field of Chemical Engineering for modelling the porous electrode film thickness in a glassy carbon based supercapacitor for electrochemical energy storage. The Lambert "W" function turned out to be the exact solution for a gas phase thermal activation process where growth of carbon film and combustion of the same film compete with each other.[14][15]
The Lambert W function was employed in the field of epitaxial film growth for the determination of the critical dislocation onset film thickness. This is the calculated thickness of an epitaxial film, where due to thermodynamic principles the film will develop crystallographic dislocations in order to minimise the elastic energy stored in the films. Prior to application of Lambert "W" for this problem, the critical thickness had to be determined via solving an implicit equation. Lambert "W" turns it in an explicit equation for analytical handling with ease
The Lambert W function has been employed in the field of fluid flow in porous media to model the tilt of an interface separating two gravitationally segregated fluids in a homogeneus tilted porous bed of constant dip and thickness where the heavier fluid, injected at the bottom end, displaces the lighter fluid that is produced at the same rate from the top end. The principal branch of the solution corresponds to stable displacements while the -1 branch applies if the displacement is unstable with the heavier fluid running underneath the ligther fluid.[17]
So the Lambert W function is natural too.