## Have You Been Taught Things Which Aren't True?

For the discussion of math. Duh.

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Suffusion of Yellow
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### Have You Been Taught Things Which Aren't True?

Last week I had a class on Liouville's theorem in complex analysis where the (usually quite excellent) professor said that it applied to any domain on C, and then used it to prove the Fundamental Theorem of Algebra. Unfortunately, as I realized later, it doesn't apply to any domain on C but only the whole plane and his proof of the FT was gibberish (in fact, it "proved" that a polynomial had infinitely many zeroes.) In short, the whole 50 minutes were filled with fake math.

And this scared me. Has something similar every happened to you? Share stories!

BlackSails
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### Re: Have You Been Taught Things Which Aren't True?

Wiki says the proof of the fundamental theorem of algebra is legit.

Suffusion of Yellow
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### Re: Have You Been Taught Things Which Aren't True?

BlackSails wrote:Wiki says the proof of the fundamental theorem of algebra is legit.

There's a real one that use the real Liouville Theorem

t0rajir0u
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### Re: Have You Been Taught Things Which Aren't True?

I think you're being too hard on your poor professor. Can't you just ask him to clarify?

kaimason1
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### Re: Have You Been Taught Things Which Aren't True?

While this is less complicated, untrue things are taught all through elementary school, untaught through middle school / high school, and then the truth comes in trickles somewhere in the meanwhile.
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hawkmp4
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### Re: Have You Been Taught Things Which Aren't True?

Can't take square roots of negative numbers...
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### Re: Have You Been Taught Things Which Aren't True?

kaimason1 wrote:While this is less complicated, untrue things are taught all through elementary school, untaught through middle school / high school, and then the truth comes in trickles somewhere in the meanwhile.

You'll see this trend continue well into post secondary as well.
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BlackSails
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### Re: Have You Been Taught Things Which Aren't True?

hawkmp4 wrote:Can't take square roots of negative numbers...

You cant, when doing math in the real numbers.

polymer
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### Re: Have You Been Taught Things Which Aren't True?

BlackSails wrote:
hawkmp4 wrote:Can't take square roots of negative numbers...

You cant, when doing math in the real numbers.

In high school when I realized this, I looked back at all my old tests and noticed they clarified that we were working with real numbers, I laughed silently to my self...

hawkmp4
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### Re: Have You Been Taught Things Which Aren't True?

Yes. But there was no mention of real or imaginary- just that the square root of negative numbers doesn't exist. Ever.
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Game_boy
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### Re: Have You Been Taught Things Which Aren't True?

A few things. Can't take factorial of anything but natural numbers; can't take the inverse sine/cosine of numbers greater than 1 or less than -1.

Can't solve cubic equations analytically - only with numerical methods. I told them about the cubic/quartic formula and they didn't believe me.

The worst one was science though: electrons orbit the nucleus like little planets.
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### Re: Have You Been Taught Things Which Aren't True?

I think a distinction needs to be made between actual mistakes and lies-to-children. The latter don't really bother me, but the former is obviously a problem.

By the way, my favorite example, courtesy of thefunniest.info:
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Lazar
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### Re: Have You Been Taught Things Which Aren't True?

skeptical scientist wrote:By the way, my favorite example, courtesy of thefunniest.info:

That has to be fake!
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BlackSails
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### Re: Have You Been Taught Things Which Aren't True?

Game_boy wrote:A few things. Can't take factorial of anything but natural numbers

You cant. The factorial is only defined on natural numbers. The gamma function is defined on all complex numbers but nonnegative integers, and is equal to the factorial for natural numbers, but its not the factorial.

The worst one was science though: electrons orbit the nucleus like little planets.

There is nothing wrong with teaching this to children. You expect them to understand modern quantum theory?

jestingrabbit
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### Re: Have You Been Taught Things Which Aren't True?

Lazar wrote:
skeptical scientist wrote:By the way, my favorite example, courtesy of thefunniest.info:

That has to be fake!

Snopes doesn't know, but points out that the date is hitler's birthday, and that the kid's name isn't light years away from adolf hitler.
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### Re: Have You Been Taught Things Which Aren't True?

BlackSails wrote:
The worst one was science though: electrons orbit the nucleus like little planets.

There is nothing wrong with teaching this to children. You expect them to understand modern quantum theory?

I think it hinders understanding of quantum theory when it is taught later on.

But here are many many many science-related lies:
nobody knows what light is, and it always goes at the speed of light, and it cannot be bent, and it is not affected by gravity.
the sun is a ball of fire, without mentioning fuel.
the periodic table is the only way to represent ongoing series in elements.

And of course the constituency of matter series:
in primary school: things are made of molecules, which are little balls.
in middle school: molecules are made of atoms, which are little balls.
in high school: atoms are made of protons, neutrons and electrons, which are little balls.
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Robstickle
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### Re: Have You Been Taught Things Which Aren't True?

That there's no method for solving equations of the form nx=m exactly where n and m are known. I think this was because the teacher didn't want us tapping that log button instead of approximating them using that method which is apparently called the bracketing method.

BlackSails
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### Re: Have You Been Taught Things Which Aren't True?

kernelpanic wrote:
BlackSails wrote:
The worst one was science though: electrons orbit the nucleus like little planets.

There is nothing wrong with teaching this to children. You expect them to understand modern quantum theory?

I think it hinders understanding of quantum theory when it is taught later on.

I think lack of math education hiders learning quantum more than an earlier model that is actually really good. Sommerfield's elliptical orbits actually gives the exact answer that you get out of the dirac equation.

t0rajir0u
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### Re: Have You Been Taught Things Which Aren't True?

It's impossible to teach physics to children without giving them oversimplified explanations of what's going on. Metaphor is an important aspect of the teaching process, and you shouldn't dismiss it just because you feel superior for knowing the "truth" (whatever that means).

The worst example I know of of actual misinformation is a teacher who insisted to his class that 1/3 was irrational.

Robstickle
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### Re: Have You Been Taught Things Which Aren't True?

That anybody in their right mind cares about writing an improper fraction as a mixed fraction. Seriously why do people teach us these things at school?

BlackSails
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### Re: Have You Been Taught Things Which Aren't True?

I was taught that it is very important to make sure that radicals ONLY appear on the top of fractions

lulzfish
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### Re: Have You Been Taught Things Which Aren't True?

BlackSails wrote:I was taught that it is very important to make sure that radicals ONLY appear on the top of fractions

Me too. I still can't imagine why.
1 / root 2 is easier to read than root 2 over 2 (sorry, can't be bothered to learn math markup), but teachers always wanted the latter.

Robstickle
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### Re: Have You Been Taught Things Which Aren't True?

And while we're on the subject my marker complained (in red ink and all) when I added a minus as opposed to just minusing. As far as I can tell he didn't knock of marks but still...come on.

kernelpanic
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### Re: Have You Been Taught Things Which Aren't True?

Robstickle wrote:That there's no method for solving equations of the form nx=m exactly where n and m are known. I think this was because the teacher didn't want us tapping that log button instead of approximating them using that method which is apparently called the bracketing method.

What!? Teachers should say "that's way above this level, but if you want to know look it up in wikipedia.". At least that's what my chem teacher says, and he is awesome.
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kaimason1
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### Re: Have You Been Taught Things Which Aren't True?

TEACHERS USE WIKIPEDIA???

They always have taught that wikipedia is all lies in my experience.

(Not offtopic at all)
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### Re: Have You Been Taught Things Which Aren't True?

kaimason1 wrote:TEACHERS USE WIKIPEDIA???

They always have taught that wikipedia is all lies in my experience.

(Not offtopic at all)

There's a difference between saying it's all lies and saying that it is untrustworthy. The math articles by-and-large are pretty good, but I have found mistakes, and there are a lot of bad non-math articles.
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kaimason1
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### Re: Have You Been Taught Things Which Aren't True?

No. They call it lies. Not 'untrustworthy', but lies.
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### Re: Have You Been Taught Things Which Aren't True?

kaimason1 wrote:No. They call it lies. Not 'untrustworthy', but lies.

If true, this would be a prime example of teachers teaching things which are untrue. But surely they just say it contains lies, rather than being all lies, no?
Last edited by skeptical scientist on Thu Mar 04, 2010 3:52 am UTC, edited 1 time in total.
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kaimason1
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### Re: Have You Been Taught Things Which Aren't True?

Exactly why I said, not offtopic.
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### Re: Have You Been Taught Things Which Aren't True?

kaimason1 wrote:TEACHERS USE WIKIPEDIA???

They always have taught that wikipedia is all lies in my experience.

(Not offtopic at all)

Yes. I did say he was awesome, didn't I? Mostly teachers in my school love wikipedia but don't recommend it for research, not because of the openness but because it is an encyclopedia. They do agree that it is the best encyclopedia to have ever appeared on Earth, though.
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kaimason1
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### Re: Have You Been Taught Things Which Aren't True?

Wow. Where do you live? I'm wondering if it is just different in Arizona.
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### Re: Have You Been Taught Things Which Aren't True?

BlackSails wrote:I was taught that it is very important to make sure that radicals ONLY appear on the top of fractions

I think it's a standardization thing, like reducing fractions so you can tell that 1/2 = 2/4

My science teacher once told me that the tide (one of them) is caused by centrifugal force.

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### Re: Have You Been Taught Things Which Aren't True?

lulzfish wrote:
BlackSails wrote:I was taught that it is very important to make sure that radicals ONLY appear on the top of fractions

Me too. I still can't imagine why.
1 / root 2 is easier to read than root 2 over 2 (sorry, can't be bothered to learn math markup), but teachers always wanted the latter.

Because it's very difficult to do long division by hand with an irrational denominator, so it became common practice to rationalize the denominator. It's a hold over from the not so distance past when calculators were uncommon.
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### Re: Have You Been Taught Things Which Aren't True?

lulzfish wrote:
BlackSails wrote:I was taught that it is very important to make sure that radicals ONLY appear on the top of fractions

Me too. I still can't imagine why.
1 / root 2 is easier to read than root 2 over 2 (sorry, can't be bothered to learn math markup), but teachers always wanted the latter.

My students still get confused when I write [imath]\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}[/imath], and they've all graduated high school and taken calculus.

Personally I don't care how my students express their answer as long as it is a) correct, and b) not in some hideously overcomplicated form. But I do wish that they could more easily translate between equivalent expressions, without giving me blank looks when I write [imath]\frac{\sqrt{45}}{5}=\frac{3}{\sqrt{5}}[/imath].
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

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### Re: Have You Been Taught Things Which Aren't True?

MrGee wrote:I think it's a standardization thing, like reducing fractions so you can tell that 1/2 = 2/4

This. Otherwise, it can be surprisingly difficult to tell when two radical expressions are the same.

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### Re: Have You Been Taught Things Which Aren't True?

BlackSails wrote:You cant. The factorial is only defined on natural numbers. The gamma function is defined on all complex numbers but nonnegative integers, and is equal to the factorial for natural numbers, but its not the factorial.

Thanks.
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### Re: Have You Been Taught Things Which Aren't True?

BlackSails wrote:The gamma function is defined on all complex numbers but nonnegative integers

Pretty sure that's not what you meant to say. ("all complex numbers but nonnegative integers" means it's *not* defined at 0, 1, 2, etc.)

In reality, it's nonpositive integers where [imath]\Gamma[/imath] is undefined.
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### Re: Have You Been Taught Things Which Aren't True?

MrGee wrote:My science teacher once told me that the tide (one of them) is caused by centrifugal force.

Isn't that like, true? At least up to arguments about whether centrifugal acts as a force.
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### Re: Have You Been Taught Things Which Aren't True?

No, tides are caused by the difference in how much the moon's gravity affects the near side of the Earth compared with the far side. Centrifugal force causes the Earth not to be spherical, but without the moon pulling differently on different parts of the water, there would be no tides.
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BlackSails
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### Re: Have You Been Taught Things Which Aren't True?

gmalivuk wrote:
BlackSails wrote:The gamma function is defined on all complex numbers but nonnegative integers

Pretty sure that's not what you meant to say. ("all complex numbers but nonnegative integers" means it's *not* defined at 0, 1, 2, etc.)

In reality, it's nonpositive integers where [imath]\Gamma[/imath] is undefined.

Right. What I meant to say was "all complex numbers but not negative integers"