I'm also confused - I was taught that "divisor" is simply the number you're dividing by, it doesn't have to be a factor - having said that I also would not have listed "1" as a "factor". On 4 Feb 2014, at 18:30, Kerry Mitchell wrote:

Okay, I'll show my ignorance. What is the difference between factor and divisor? The terms are commonly used interchangeably, even at MathWorld.

Kerry

On Tue, Feb 4, 2014 at 11:22 AM, Bill Gosper <billgosper@gmail.com> wrote:

...

I just failed to Google up any outrage over an infuriating TV quiz show I mistakenly watched several years ago. The contestant, (former astronaut Rusty Schweikart?) sailed right through to the million dollar question without even using his two "lifelines(?)", and then was sent home penniless for not listing 1 among the "factors" of 6. I wonder if, had he mentioned 1, they would have screwed him for confusing "factors" with "divisors".

Anyway, ("drill and kill") Saxon Math is apparently using "factor" to mean divisor, presumably because it has fewer syllables:

"Write the factors of 10 that are also factors of 15."

Sounds like they are expecting a "factor" of 1. (I should've checked if they think 1 is a prime.)

In the same assignment,

"Divide 20/9. Write the quotient as a fraction." "Divide and write the quotient as a fraction: 25/6"

It would probably be less harmful if they signaled their intent with gestures and whistles, as in canine obedience school.

--rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.

________________________________ From: Andy Latto <andy.latto@pobox.com> To: Eugene Salamin <gene_salamin@yahoo.com>; math-fun <math-fun@mailman.xmission.com> Sent: Tuesday, February 4, 2014 11:38 AM Subject: Re: [math-fun] More 4th grade "math"

On Tue, Feb 4, 2014 at 2:12 PM, Eugene Salamin <gene_salamin@yahoo.com> wrote:

...

According to a friend who volunteers in the Santa Cruz CA Public Schools, the official view is that 1 is a prime, because its only divisors are 1 and itself.  However, a teacher did mention that in more advanced mathematics, 1 is not a prime.

Do they also teach that unique factorization is false? Or is it stated as "numbers > 1 have a unique factorization into primes other than 1"?

Andy

They do not say anything at all about unique factorization.

  --  Gene

Back in 1914 the number 1 was a prime. At least according to D. N. Lehmer. See D. N. Lehmer, List of primes numbers from 1 to 10,006,721, Carnegie Institution Washington, D.C., 1914 On Tue, Feb 4, 2014 at 1:38 PM, Andy Latto <andy.latto@pobox.com> wrote:

On Tue, Feb 4, 2014 at 2:12 PM, Eugene Salamin <gene_salamin@yahoo.com> wrote:

...

According to a friend who volunteers in the Santa Cruz CA Public Schools, the official view is that 1 is a prime, because its only divisors are 1 and itself. However, a teacher did mention that in more advanced mathematics, 1 is not a prime.

Do they also teach that unique factorization is false? Or is it stated as "numbers > 1 have a unique factorization into primes other than 1"?

Andy

_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

Someone should write a book for college teachers that explains what misinformation students commonly carry with them when they arrive at college. I'm sure there's a lot of variety here, with some students for instance thinking that squares aren't rectangles and others thinking that they are rectangles, and of course some thinking that 1 is prime and others thinking that it isn't. It could double as a book for first year college students, too, I guess, though I suspect that the two target audiences are sufficiently different that two different books are called for. Jim Propp On Tuesday, February 4, 2014, Michael Greenwald <mbgreen@seas.upenn.edu> wrote:

I'm sorry to boggle about a non-essential part of this anecdote, but was the "million dollar question" really list the factors of 6? Or was that a small part of a larger, more interesting question? It is really hard to believe a question so simple (but apparently not so straightforward) was really the apex of a struggle for 1 million dollars...

(Incidentally, about the "factor" vs. "divisor" question: when I was in elementary school factor and "proper divisor" interchangeably referred to integers that divided a number "equally", while "prime factor" meant exactly what you'd expect. (Divisor without any qualifier (just like dividend and quotient) could be *any* number --- well, other than 0).)

On 2014-02-04 10:22, Bill Gosper wrote:

...

I just failed to Google up any outrage over an infuriating TV quiz show I mistakenly watched several years ago. The contestant, (former astronaut Rusty Schweikart?) sailed right through to the million dollar question without even using his two "lifelines(?)", and then was sent home penniless for not listing 1 among the "factors" of 6. I wonder if, had he mentioned 1, they would have screwed him for confusing "factors" with "divisors".

Anyway, ("drill and kill") Saxon Math is apparently using "factor" to mean divisor, presumably because it has fewer syllables:

"Write the factors of 10 that are also factors of 15."

Sounds like they are expecting a "factor" of 1. (I should've checked if they think 1 is a prime.)

In the same assignment,

"Divide 20/9 <x-apple-data-detectors://4>. Write the quotient as a fraction." "Divide and write the quotient as a fraction: 25/6<x-apple-data-detectors://5> "

It would probably be less harmful if they signaled their intent with gestures and whistles, as in canine obedience school.

--rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

The two are surely distinct categories, but for each axiom there is a theorem stating its result -- and such theorem, of course, has a one-step proof. Charles Greathouse Analyst/Programmer Case Western Reserve University On Tue, Feb 4, 2014 at 6:12 PM, meekerdb <meekerdb@verizon.net> wrote:

I had an argument just last year with a physicist who insisted that axioms weren't theorems.

Brent Meeker

On 2/4/2014 2:59 PM, James Propp wrote:

...

Someone should write a book for college teachers that explains what misinformation students commonly carry with them when they arrive at college. I'm sure there's a lot of variety here, with some students for instance thinking that squares aren't rectangles and others thinking that they are rectangles, and of course some thinking that 1 is prime and others thinking that it isn't. It could double as a book for first year college students, too, I guess, though I suspect that the two target audiences are sufficiently different that two different books are called for.

Jim Propp

On Tuesday, February 4, 2014, Michael Greenwald <mbgreen@seas.upenn.edu> wrote:

I'm sorry to boggle about a non-essential part of this anecdote, but was

...

the "million dollar question" really list the factors of 6? Or was that a small part of a larger, more interesting question? It is really hard to believe a question so simple (but apparently not so straightforward) was really the apex of a struggle for 1 million dollars...

(Incidentally, about the "factor" vs. "divisor" question: when I was in elementary school factor and "proper divisor" interchangeably referred to integers that divided a number "equally", while "prime factor" meant exactly what you'd expect. (Divisor without any qualifier (just like dividend and quotient) could be *any* number --- well, other than 0).)

On 2014-02-04 10:22, Bill Gosper wrote:

I just failed to Google up any outrage over an infuriating TV quiz show

...

I mistakenly watched several years ago. The contestant, (former astronaut Rusty Schweikart?) sailed right through to the million dollar question without even using his two "lifelines(?)", and then was sent home penniless for not listing 1 among the "factors" of 6. I wonder if, had he mentioned 1, they would have screwed him for confusing "factors" with "divisors".

Anyway, ("drill and kill") Saxon Math is apparently using "factor" to mean divisor, presumably because it has fewer syllables:

"Write the factors of 10 that are also factors of 15."

Sounds like they are expecting a "factor" of 1. (I should've checked if they think 1 is a prime.)

In the same assignment,

"Divide 20/9 <x-apple-data-detectors://4>. Write the quotient as a fraction." "Divide and write the quotient as a fraction: 25/6<x-apple-data-detectors://5> "

It would probably be less harmful if they signaled their intent with gestures and whistles, as in canine obedience school.

--rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

One error I believed for many years* is that the antiderivative of 1/x is ln|x| + C. --Dan ______________________________________________ * Thanks to my misplaced trust in G.B. Thomas. On 2014-02-04, at 2:59 PM, James Propp wrote:

Someone should write a book for college teachers that explains what misinformation students commonly carry with them when they arrive at college.

[Dan Asimov:]

One error I believed for many years* is that the antiderivative of 1/x is ln|x| + C.

[Scott Huddleston:]

I'll bite. What's the error?

Two different constants, one on each side of zero. -- g

Well, as I see it, the definition of antiderivative of a function g is a function f such that f is differentiable and f'(x) = g(x) for all x in the domain of f. Now, 1/x is defined on R - {0}. And on that set, the most general antiderivative of 1/x is ln( x) + C_1, x > 0 f(x) = ln(-x) + C_2, x < 0 --Dan On 2014-02-04, at 7:11 PM, Eugene Salamin wrote:

As long as you don't cross the singularity at 0, G. B. Thomas is correct. Assume b > a > 0.

int(1/x, x=-b..-a) = -int(1/x, x=a..b) = -log(b/a).

log|-a| - log|-b| = log a - log b = -log(b/a).

If you do cross the singularity, then in integral has no well defined limit.

I wrote: ----- One error I believed for many years* is that the antiderivative of 1/x is ln|x| + C. --Dan ______________________________________________ * Thanks to my misplaced trust in G.B. Thomas. -----

I would add to what Jim says to highlight differences in such definitions between Maths syllabuses in different countries..... On 4 Feb 2014, at 22:59, James Propp wrote:

Someone should write a book for college teachers that explains what misinformation students commonly carry with them when they arrive at college. I'm sure there's a lot of variety here, with some students for instance thinking that squares aren't rectangles and others thinking that they are rectangles, and of course some thinking that 1 is prime and others thinking that it isn't. It could double as a book for first year college students, too, I guess, though I suspect that the two target audiences are sufficiently different that two different books are called for.

Jim Propp

On Tuesday, February 4, 2014, Michael Greenwald <mbgreen@seas.upenn.edu> wrote:

...

I'm sorry to boggle about a non-essential part of this anecdote, but was the "million dollar question" really list the factors of 6? Or was that a small part of a larger, more interesting question? It is really hard to believe a question so simple (but apparently not so straightforward) was really the apex of a struggle for 1 million dollars...

(Incidentally, about the "factor" vs. "divisor" question: when I was in elementary school factor and "proper divisor" interchangeably referred to integers that divided a number "equally", while "prime factor" meant exactly what you'd expect. (Divisor without any qualifier (just like dividend and quotient) could be *any* number --- well, other than 0).)

On 2014-02-04 10:22, Bill Gosper wrote:

...

I just failed to Google up any outrage over an infuriating TV quiz show I mistakenly watched several years ago. The contestant, (former astronaut Rusty Schweikart?) sailed right through to the million dollar question without even using his two "lifelines(?)", and then was sent home penniless for not listing 1 among the "factors" of 6. I wonder if, had he mentioned 1, they would have screwed him for confusing "factors" with "divisors".

Anyway, ("drill and kill") Saxon Math is apparently using "factor" to mean divisor, presumably because it has fewer syllables:

"Write the factors of 10 that are also factors of 15."

Sounds like they are expecting a "factor" of 1. (I should've checked if they think 1 is a prime.)

In the same assignment,

"Divide 20/9 <x-apple-data-detectors://4>. Write the quotient as a fraction." "Divide and write the quotient as a fraction: 25/6<x-apple-data-detectors://5> "

It would probably be less harmful if they signaled their intent with gestures and whistles, as in canine obedience school.

--rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.