Re: Metric Conversions
On Sat, 10 Jan 2009, David Hobby wrote:
> Back to what I was saying about Wikipedia, the
> article there at
> http://en.wikipedia.org/wiki/Natural_number
> starts like this:
>
>> In mathematics, a natural number (also called counting number) can
>> mean either an element of the set {1, 2, 3, ...} (the positive
>> integers) or an element of the set {0, 1, 2, 3, ...} (the
>> non-negative integers). The latter is especially preferred in
>> mathematical logic, set theory, and computer science.
>
> I often teach upper division college Math courses that
> are just at the cusp between the two definitions, and
> make a point of stating the definition of the natural
> numbers. (Whatever it says in the text, of course!)
>
> ---David
>
> Positive integers, Maru
Positive, or nonnegative? That is the question
Julia
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Re: Metric Conversions
Ray & Maree Ludenia wrote:
> David Hobby wrote:
>> Another place where this kind of thing shows
>> up is in the definition of the natural numbers.
>> Do they start at 0 or at 1? On a basic level,
>> starting at 1 makes sense. But in set theory
>> (or computer science) starting at 0 works better.
>>
>
> David,
> I was only a maths teacher in an Australian High School, but we taught that
> natural numbers start at 1. If you want to include 0 then they were called
> whole numbers. It is only a name after all, but we were careful to make that
> distinction to 12 year old students. Do they make the same distinction here?
Maree--
Hi. If you're teaching that the natural numbers
start at 1, then "whole numbers" is what you call the
set that includes 0. That usage is standard at the high
school level.
Back to what I was saying about Wikipedia, the
article there at
http://en.wikipedia.org/wiki/Natural_number
starts like this:
> In mathematics, a natural number (also called counting number) can
> mean either an element of the set {1, 2, 3, ...} (the positive
> integers) or an element of the set {0, 1, 2, 3, ...} (the
> non-negative integers). The latter is especially preferred in
> mathematical logic, set theory, and computer science.
I often teach upper division college Math courses that
are just at the cusp between the two definitions, and
make a point of stating the definition of the natural
numbers. (Whatever it says in the text, of course!)
---David
Positive integers, Maru
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RE: Metric Conversions
David Hobby wrote: > > Another place where this kind of thing shows > up is in the definition of the natural numbers. > Do they start at 0 or at 1? On a basic level, > starting at 1 makes sense. But in set theory > (or computer science) starting at 0 works better. > David, I was only a maths teacher in an Australian High School, but we taught that natural numbers start at 1. If you want to include 0 then they were called whole numbers. It is only a name after all, but we were careful to make that distinction to 12 year old students. Do they make the same distinction here? [Including fractions and decimals was the set of (positive) rational numbers. As students' mathematical knowledge progressed we taught them about negative rational numbers and a year later they were introduced to irrational numbers.] The 0/1 confusion was an issue in teaching sequences and difference equations to our older students, especially in calculating the number of terms, but that is another problem altogether. Maree Ludenia ___ http://www.mccmedia.com/mailman/listinfo/brin-l
RE: Metric Conversions
> > Seems like a reasonable question to me, Max. > How many litres are there in a liter? > African or European? Dan M. ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Metric Conversions
On Jan 9, 2009, at 8:47 AM, David Hobby wrote: >> And some of us became accustomed at an early age to integer number >> systems that wrap around from (2^n)-1 to -2^n, for various relatively >> small values of n. :) > > For some values of "early"? I don't think kindergarteners > count "1, 2, 3, -4, -3, ...". : ) > > ---David Only on cheap two-bit computers. :) (Well, actually, that would be a cheap 3-bit computer..) Running into the 32767 -> -32768 wraparound was definitely an annoyance, though. (At the time, the environment I was playing in didn't have anything corresponding to a longint type, and I was just starting to find that wraparound a fairly seriously crippling limitation. It was only later that I learned about precision integer techniques, and they wouldn't have been feasible in the language or on the hardware I was using at the time anyway.) But having grown up with discreteness of that sort made my later approach to more theoretical math a bit .. odd. :D ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Metric Conversions
Bruce Bostwick wrote: > On Jan 9, 2009, at 8:15 AM, David Hobby wrote: ... >> The crude answer to you would be to say: >> "Oh, so it means that? Then go edit Wikipedia >> to say so." See: >> http://en.wikipedia.org/wiki/Linear_transformation >> >> That's a great function of Wikipedia--standardizing >> nomenclature. >> >> ---David > > To the extent to which nomenclature can be standardized, that is. > (Some terms have overlapping and somewhat incompatible definitions > across the namespaces of different specialties, and sometimes all that > can be done to remove the ambiguity is specify the namespace. :) Bruce-- Oh, of course. Wikipedia is full of disambiguation pages. So I guess a better statement would be that a meaning should be at least listed on Wikipedia as an alternative. For instance, I have a co-author who wanted to use a non-standard definition of the Catalan numbers in our paper. (They're a sequence of integers, and it's that classic problem: do you start with the 1st one or with the 0th one?) Pointing out that Wikipedia gave a different definition was a quick way to settle the issue. Quicker than using some particular paper encyclopedia would have been, since to be fair I'd have to look up the Catalan numbers in a bunch of them. > And some of us became accustomed at an early age to integer number > systems that wrap around from (2^n)-1 to -2^n, for various relatively > small values of n. :) For some values of "early"? I don't think kindergarteners count "1, 2, 3, -4, -3, ...". : ) ---David ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Metric Conversions
On Jan 9, 2009, at 8:15 AM, David Hobby wrote: > Ronn! Blankenship wrote: > ... >>> But I did know there had to be one. I think >>> these are called "affine" transformations. >>> (Linear is x --> ax, and Affine is x --> ax + b.) >> >> y = mx + b is a linear equation. (With slope m and y-intercept b.) >> >> . . . ronn! :) > > Ronn-- > > Why, yes it is. But "linear transformation" > has a different meaning. This is one of those > places where usage may differ between simple > and advanced Math. Once people got into > doing transformations to vector spaces by > matrix multiplication, they decided that they > wanted to define "T is linear" as > "T(ax + by) = a T(x) + b T(y) always holds". > Once you do that, T(0) = 0, and you don't > get to add a constant as part of a linear > transformation. > > Another place where this kind of thing shows > up is in the definition of the natural numbers. > Do they start at 0 or at 1? On a basic level, > starting at 1 makes sense. But in set theory > (or computer science) starting at 0 works better. > > The crude answer to you would be to say: > "Oh, so it means that? Then go edit Wikipedia > to say so." See: > http://en.wikipedia.org/wiki/Linear_transformation > > That's a great function of Wikipedia--standardizing > nomenclature. > > ---David To the extent to which nomenclature can be standardized, that is. (Some terms have overlapping and somewhat incompatible definitions across the namespaces of different specialties, and sometimes all that can be done to remove the ambiguity is specify the namespace. :) And some of us became accustomed at an early age to integer number systems that wrap around from (2^n)-1 to -2^n, for various relatively small values of n. :) Overflow bit Maru ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Metric Conversions
Ronn! Blankenship wrote: ... >> But I did know there had to be one. I think >> these are called "affine" transformations. >> (Linear is x --> ax, and Affine is x --> ax + b.) > > y = mx + b is a linear equation. (With slope m and y-intercept b.) > > . . . ronn! :) Ronn-- Why, yes it is. But "linear transformation" has a different meaning. This is one of those places where usage may differ between simple and advanced Math. Once people got into doing transformations to vector spaces by matrix multiplication, they decided that they wanted to define "T is linear" as "T(ax + by) = a T(x) + b T(y) always holds". Once you do that, T(0) = 0, and you don't get to add a constant as part of a linear transformation. Another place where this kind of thing shows up is in the definition of the natural numbers. Do they start at 0 or at 1? On a basic level, starting at 1 makes sense. But in set theory (or computer science) starting at 0 works better. The crude answer to you would be to say: "Oh, so it means that? Then go edit Wikipedia to say so." See: http://en.wikipedia.org/wiki/Linear_transformation That's a great function of Wikipedia--standardizing nomenclature. ---David ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Metric Conversions
At 09:17 PM Thursday 1/8/2009, David Hobby wrote: >Ronn! Blankenship wrote: > > At 05:34 PM Thursday 1/8/2009, Rceeberger wrote: > >> http://xkcd.com/526/ > >> > >> xponent > >> Spit Goes Cunk Maru > >> rob > > > > > > I presume everybody here already knows that -40°C = -40°F. > > > > > > Linear Transformation Fixed Point Maru > >Ronn!-- No, I didn't know that it was at -40. > >But I did know there had to be one. I think >these are called "affine" transformations. >(Linear is x --> ax, and Affine is x --> ax + b.) y = mx + b is a linear equation. (With slope m and y-intercept b.) . . . ronn! :) ___ http://www.mccmedia.com/mailman/listinfo/brin-l
Re: Metric Conversions
On 09/01/2009, at 5:51 PM, Wayne Eddy wrote: > - Original Message - > From: "Max Battcher" > To: "Killer Bs (David Brin et al) Discussion" > Sent: Friday, January 09, 2009 10:47 AM > Subject: Re: Metric Conversions > > >> I have to say that the best one of the lot is the 3L -- 2-Liter >> Bottle. >> It's always funny when someone asks how big a 2-Liter Bottle is in >> metric... 3 Liters is a better response than some of the ones I've >> used. > >> --Max Battcher-- > > Seems like a reasonable question to me, Max. > How many litres are there in a liter? It depends who's asking. But a quart is usually a good approximate answer ;) > > Regards, > > Wayne ___ http://www.mccmedia.com/mailman/listinfo/brin-l
