[math-fun] Draft of my February 2017 blog post
Date: 2017-02-14 09:16 From: Nick Baxter <nickb@baxterweb.com> To: math-fun <math-fun@mailman.xmission.com> Reply-To: math-fun <math-fun@mailman.xmission.com>
ok, someone has to ask...factor and divisor are the same thing;
Argh! I had no idea how many people believe this!
why are you implying otherwise?
Because they're different!
I know there is potential confusion with prime factor and factorization, but they're different issues.
Nick
Primality isn't the issue. How many factors of 6 are there in 12? How many factors of 1? 1 is not a goddam factor of anything. --rwg
Errm ... my esteemed colleague's enthusiasm for his subject occasionally gets the better of him. I venture to suggest that it must be quite impossible for anybody outside hardcore number theory to comprehend why these distinctions matter in the slightest, let alone cause steam to issue from various anatomical orifices. Specialists of any field need to beware of attempting to co-opt for a highly technical purpose any term previously in common use for a less constrained notion. Some etymologically challenged analyst's decision to christen infinite sums "series" --- a usage fortunately now largely abandoned --- hardly confers on the rest of humanity any obligation to refrain from continuing to conflate that word with "sequence", even in a mathematical context. Also similar situations occur routinely elsewhere: for example it is frequently important to distinguish between singular and nonsingular square matrices, without any perceived necessity to concoct separate terms for the two cases. What's wrong with (say) "non-unit" divisor/factor, whenever called for? WFL On 2/15/17, Bill Gosper <billgosper@gmail.com> wrote:
Date: 2017-02-14 09:16 From: Nick Baxter <nickb@baxterweb.com> To: math-fun <math-fun@mailman.xmission.com> Reply-To: math-fun <math-fun@mailman.xmission.com>
ok, someone has to ask...factor and divisor are the same thing;
Argh! I had no idea how many people believe this!
why are you implying otherwise?
Because they're different!
I know there is potential confusion with prime factor and factorization, but they're different issues.
Nick
Primality isn't the issue. How many factors of 6 are there in 12? How many factors of 1? 1 is not a goddam factor of anything. --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
I was not at all aware that "series" is not a current term for a (usually) infinite sum. —Dan
On Feb 14, 2017, at 8:08 PM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Errm ... my esteemed colleague's enthusiasm for his subject occasionally gets the better of him. I venture to suggest that it must be quite impossible for anybody outside hardcore number theory to comprehend why these distinctions matter in the slightest, let alone cause steam to issue from various anatomical orifices.
Specialists of any field need to beware of attempting to co-opt for a highly technical purpose any term previously in common use for a less constrained notion. Some etymologically challenged analyst's decision to christen infinite sums "series" --- a usage fortunately now largely abandoned --- hardly confers on the rest of humanity any obligation to refrain from continuing to conflate that word with "sequence", even in a mathematical context.
Also similar situations occur routinely elsewhere: for example it is frequently important to distinguish between singular and nonsingular square matrices, without any perceived necessity to concoct separate terms for the two cases. What's wrong with (say) "non-unit" divisor/factor, whenever called for?
WFL
On 2/15/17, Bill Gosper <billgosper@gmail.com> wrote:
Date: 2017-02-14 09:16 From: Nick Baxter <nickb@baxterweb.com> To: math-fun <math-fun@mailman.xmission.com> Reply-To: math-fun <math-fun@mailman.xmission.com>
ok, someone has to ask...factor and divisor are the same thing;
Argh! I had no idea how many people believe this!
why are you implying otherwise?
Because they're different!
I know there is potential confusion with prime factor and factorization, but they're different issues.
Nick
Primality isn't the issue. How many factors of 6 are there in 12? How many factors of 1? 1 is not a goddam factor of anything. --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
If it isn't, then the Mathematical Tripos is outdated: https://www.maths.cam.ac.uk/undergrad/course/schedules.pdf Also, the terms 'Fourier series', 'Taylor series', and 'Dirichlet L-series' are still in use. Best wishes, Adam P. Goucher
Sent: Wednesday, February 15, 2017 at 5:10 AM From: "Dan Asimov" <asimov@msri.org> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Draft of my February 2017 blog post
I was not at all aware that "series" is not a current term for a (usually) infinite sum.
—Dan
On Feb 14, 2017, at 8:08 PM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Errm ... my esteemed colleague's enthusiasm for his subject occasionally gets the better of him. I venture to suggest that it must be quite impossible for anybody outside hardcore number theory to comprehend why these distinctions matter in the slightest, let alone cause steam to issue from various anatomical orifices.
Specialists of any field need to beware of attempting to co-opt for a highly technical purpose any term previously in common use for a less constrained notion. Some etymologically challenged analyst's decision to christen infinite sums "series" --- a usage fortunately now largely abandoned --- hardly confers on the rest of humanity any obligation to refrain from continuing to conflate that word with "sequence", even in a mathematical context.
Also similar situations occur routinely elsewhere: for example it is frequently important to distinguish between singular and nonsingular square matrices, without any perceived necessity to concoct separate terms for the two cases. What's wrong with (say) "non-unit" divisor/factor, whenever called for?
WFL
On 2/15/17, Bill Gosper <billgosper@gmail.com> wrote:
Date: 2017-02-14 09:16 From: Nick Baxter <nickb@baxterweb.com> To: math-fun <math-fun@mailman.xmission.com> Reply-To: math-fun <math-fun@mailman.xmission.com>
ok, someone has to ask...factor and divisor are the same thing;
Argh! I had no idea how many people believe this!
why are you implying otherwise?
Because they're different!
I know there is potential confusion with prime factor and factorization, but they're different issues.
Nick
Primality isn't the issue. How many factors of 6 are there in 12? How many factors of 1? 1 is not a goddam factor of anything. --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
From: page 14 of "Introduction to Analytic Number Theory" by Tom Apostol (1976) . (Note the text "evolved from a course offered at the California Institute of Tecchnology during the last 25 years.") Notation. In this chapter, small latin letters a,b,c,d,n,etc., denote
integers; they can be positive, negative or zero.
Definition of divisibility. We say d divides n and we write d|n whenever n = cd for some c. We also say that n is a multiple of d, that d is a divisor of n, or that d is a factor of n.
It would be interesting to see a reference to a publication that denies that 1 is a factor of every integer. On Tue, Feb 14, 2017 at 8:31 PM, Bill Gosper <billgosper@gmail.com> wrote:
Date: 2017-02-14 09:16 From: Nick Baxter <nickb@baxterweb.com> To: math-fun <math-fun@mailman.xmission.com> Reply-To: math-fun <math-fun@mailman.xmission.com>
ok, someone has to ask...factor and divisor are the same thing;
Argh! I had no idea how many people believe this!
why are you implying otherwise?
Because they're different!
I know there is potential confusion with prime factor and factorization, but they're different issues.
Nick
Primality isn't the issue. How many factors of 6 are there in 12? How many factors of 1? 1 is not a goddam factor of anything. --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
W. Edwin Clark: "It would be interesting to see a reference to a publication that denies that 1 is a factor of every integer." The 19th century arithmetic texts that I had occasion to look at all agreed that both the multiplicand and multiplier of a product were factors and generally gave examples in pairs that excluded the number itself multiplied by one. Edward Liddell in his Arithmetic for the Use of Schools (1860) made it explicit: "We have already learnt that when 6 and 8 are multiplied together they make the product 48. For this reason 6 and 8 are called factors of 48, from the Latin facio, which signifies to make. We may therefore separate or resolve 48 into the two factors 6 and 8, or into the two factors 4 and 12. The figure 1 is not regarded as a factor; consequently, in whole numbers, all factors are greater than unity." Eric Weisstein cites Ore's 1988 Number Theory and its History and Burton's 1989 Elementary Number Theory for his number theoretic usage that "a factor of a number n is equivalent to a divisor of n". He adds: "In elementary education, the term 'factor' is sometimes used to mean proper divisor, i.e., a factor of n other than the number itself. However, as a result of the confusion this practice creates and its inconsistency with the mathematical literature, it should be discouraged."
participants (6)
-
Adam P. Goucher -
Bill Gosper -
Dan Asimov -
Fred Lunnon -
Hans Havermann -
W. Edwin Clark