Have You Been Taught Things Which Aren't True?

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

Postby antonfire » Fri Nov 19, 2010 11:02 am UTC

I've seen something like [imath]Z_{\geq 0}[/imath] used to denote the set of nonnegative integers.
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Re: Have You Been Taught Things Which Aren't True?

Postby voidPtr » Fri Nov 19, 2010 5:57 pm UTC

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

Somewhere between Grade 6 and 8 I was taught 1 was a prime number and believed it all the way up to my second year of university.

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

Postby snowyowl » Tue Nov 23, 2010 1:52 am UTC

jestingrabbit wrote:I used [imath]N^+[/imath] and [imath]N_0[/imath] for the two sets in question. It worked well enough.

Different countries seem to have different notations. I originally learned that [imath]N[/imath] was the set of nonnegative integers, [imath]N^*[/imath] the set of positive integers, [imath]Z[/imath] the set of integers, and [imath]Z^*[/imath] the set of nonzero integers. I'll let you guess what [imath]Q^*[/imath], [imath]R^*[/imath] and [imath]C^*[/imath] were. It was very confusing when I moved from France to England and had to use new notations. Fortunately the distinction doesn't come up that often, so I can usually get away with small mistakes.

Oh, and [imath]R^+[/imath] was the nonnegative reals. The positive reals only ever came up once... [imath]R^{+*}[/imath] (mind blown)
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Re: Have You Been Taught Things Which Aren't True?

Postby letterX » Tue Nov 23, 2010 2:01 am UTC

snowyowl wrote:The positive reals only ever came up once... [imath]R^{+*}[/imath] (mind blown)

Really? That's where [imath]\epsilon[/imath] lives (right down the street from [imath]\delta[/imath]).

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

Postby Tirian » Tue Nov 23, 2010 2:51 am UTC

Ugh, I was just reminded of the worst one in class today.

You know that symbol that we taught you was the symbol for the operation of multiplication? Two slashed lines that cross each other? Yeah ... change of plans. We need that symbol to be our go-to variable now that we're learning algebra. Multiplication is now a dot, if we do anything at all. No, not a decimal point, a little higher than that....

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

Postby Sizik » Tue Nov 23, 2010 2:57 am UTC

Tirian wrote:Ugh, I was just reminded of the worst one in class today.

You know that symbol that we taught you was the symbol for the operation of multiplication? Two slashed lines that cross each other? Yeah ... change of plans. We need that symbol to be our go-to variable now that we're learning algebra. Multiplication is now a dot, if we do anything at all. No, not a decimal point, a little higher than that....


Don't worry, you'll get to use it again *coughincollegecough* when you learn about vectors.
Can't say the same about ÷ though.
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Re: Have You Been Taught Things Which Aren't True?

Postby skullturf » Tue Nov 23, 2010 3:05 am UTC

I actually use ÷ when I teach university students, believe it or not!

I often use it when I teach the ratio test, and I have one moderately large fraction divided by another. In such situations, writing one large fraction above another sometimes looks too cluttered, and putting a / between them is somehow less visually appealing to me than the ÷ symbol.

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

Postby Eebster the Great » Tue Nov 23, 2010 3:12 am UTC

Sizik wrote:
Tirian wrote:Ugh, I was just reminded of the worst one in class today.

You know that symbol that we taught you was the symbol for the operation of multiplication? Two slashed lines that cross each other? Yeah ... change of plans. We need that symbol to be our go-to variable now that we're learning algebra. Multiplication is now a dot, if we do anything at all. No, not a decimal point, a little higher than that....


Don't worry, you'll get to use it again *coughincollegecough* when you learn about vectors.
Can't say the same about ÷ though.

I'm not sure why ÷ and × are still taught first. Admittedly, ÷ has the advantage of being essentially unambiguous, but if it isn't used that isn't relevant. And × is just fraught with problems (though it is usually pretty clear in the case of cross-products).

· is marginally better, but still looks strange seeing things like · : R × R → R. I mean in general, the middle dot looks strange when not placed between two factors.

In a final note, did anybody here actually learn the terms "minuend" and "subtrahend" from anywhere other than Wikipedia (or this post)?

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

Postby Tirian » Tue Nov 23, 2010 3:26 am UTC

Eebster the Great wrote:· is marginally better, but still looks strange seeing things like · : R × R → R. I mean in general, the middle dot looks strange when not placed between two factors.

In a final note, did anybody here actually learn the terms "minuend" and "subtrahend" from anywhere other than Wikipedia (or this post)?


[imath]((x,y)\mapsto xy):R\times R\rightarrow R[/imath] is your friend.

I did learn those words (and summand and multiplier and multiplicand and divisor and dividend) back in the time. I think these are some of those "Are You Smarter Than A Third Grader" factoids that are so alarmingly useless that forgetting them is a sign of maturity.

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

Postby Eebster the Great » Tue Nov 23, 2010 3:58 am UTC

Tirian wrote:multiplier and multiplicand

Why not just "factor?" It is commutative after all . . .

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

Postby Mike_Bson » Tue Nov 23, 2010 4:17 am UTC

I learned about nullity in 3rd grade.

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

Postby mdyrud » Tue Nov 23, 2010 5:10 am UTC

I learned all of those terms in math. I always complained that they were totally pointless to learn. My mom said I had to, and that they would be useful to know at some point. I am now a freshman in college majoring in mathematics, and the only time I have used one of those terms was to answer a single Knowledge Bowl question in a round that we won handily anyway.

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

Postby Tirian » Tue Nov 23, 2010 7:54 am UTC

Eebster the Great wrote:
Tirian wrote:multiplier and multiplicand

Why not just "factor?" It is commutative after all . . .


Because the process that you're teaching at the time is applying the distributive law by decomposing the multiplicand and separately multiplying each "digit" by the multiplier. In contrast, each summand in addition has the same role in the process. You'd get the same answer if you traded the two numbers before multiplying, but as a famous mathematician once noted, the idea is to understand what you're doing and not to get the right answer.

(Odd note of the evening: Firefox's spell checker recognizes "multiplicand" but not "summand".)

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

Postby Darryl » Tue Nov 23, 2010 2:34 pm UTC

voidPtr wrote:"Have You Been Taught Things Which Aren't True?"

Somewhere between Grade 6 and 8 I was taught 1 was a prime number and believed it all the way up to my second year of university.

I talked to someone whose college professor taught her that you include 1 in prime factorizations, and that 1 is not relatively prime to every number. (Since relatively prime is defined as gcd(a,b) = 1, and gcd (1,x) = 1)
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Re: Have You Been Taught Things Which Aren't True?

Postby skullturf » Tue Nov 23, 2010 4:01 pm UTC

Darryl wrote:I talked to someone whose college professor taught her that you include 1 in prime factorizations


How many times? :D

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

Postby Darryl » Tue Nov 23, 2010 4:05 pm UTC

skullturf wrote:
Darryl wrote:I talked to someone whose college professor taught her that you include 1 in prime factorizations


How many times? :D

I don't know, but she nearly screwed up someone's Discrete Math take-home quiz as she was walking by.
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Re: Have You Been Taught Things Which Aren't True?

Postby larryllama » Tue Nov 23, 2010 5:23 pm UTC

My Advanced Calculus professor tried to teach us that the Continuum Hypothesis had been proven to be true. I knew better and pointed it out after class. In fairness, when he graduated it was thought to be true but at that time had only been proven that it can't be dis-proven. It was later proven that it can't be proven either.

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

Postby Eebster the Great » Tue Nov 23, 2010 5:26 pm UTC

Tirian wrote:
Eebster the Great wrote:
Tirian wrote:multiplier and multiplicand

Why not just "factor?" It is commutative after all . . .


Because the process that you're teaching at the time is applying the distributive law by decomposing the multiplicand and separately multiplying each "digit" by the multiplier. In contrast, each summand in addition has the same role in the process. You'd get the same answer if you traded the two numbers before multiplying, but as a famous mathematician once noted, the idea is to understand what you're doing and not to get the right answer.

Well generally in elementary school kids don't understand what they are doing at all, they are just told that the process works so they accept it. It isn't really until you start talking about how base 10 representations work (which I can't envision happening before maybe fifth grade) that you have any chance of really understanding the process.

EDIT: So it looks like the idea isn't to distinguish between factors in columnar multiplication but in the simple concept of "xy means you have a sum of y x's." That is, 5*3 = 5 + 5 + 5. So 5 is the multiplicand (that which is to be multiplied) and 3 is the multiplier (that which multiplies). I guess this does make some conceptual sense for integers.

(Odd note of the evening: Firefox's spell checker recognizes "multiplicand" but not "summand".)

Because most people use the term "addend."


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