-----Original Message----- From: John Conway [mailto:conway@Math.Princeton.EDU] Sent: Wednesday, October 29, 2003 4:55 PM To: math-fun Subject: Re: [math-fun] Simple EF
On Wed, 29 Oct 2003, Jon Perry wrote:
This may be completely dumb, but is it always possible to solve x/y = a/b + c/d, where all algebraic quantities are positive integers, for all x and y?
How about a=x, b=y, c=0, d=1 ? John Conway
0 isn't a positive integer. But how about a=c=x, b=d=2y? Andy Latto andy.latto@pobox.com
On Wed, 29 Oct 2003, Andy Latto wrote:
On Wed, 29 Oct 2003, Jon Perry wrote:
This may be completely dumb, but is it always possible to solve x/y = a/b + c/d, where all algebraic quantities are positive integers, for all x and y?
How about a=x, b=y, c=0, d=1 ? John Conway
0 isn't a positive integer. But how about a=c=x, b=d=2y?
Oop! Thanks. JHC
On Wed, 29 Oct 2003, Alec Mihailovs wrote:
On Behalf Of Andy Latto
0 isn't a positive integer.
I was told that 0 is a positive integer in France though...
It's a pity that "positive" is defined exclusively, but I don't think we can afford to change it. I rather doubt that 0 is counted as positive in France - what I expect the remark refers to is "natural number", whose meaning is changing from the exclusive to the inclusive sense, and seems to have largely done so already in France. What we ought to do, is find an existing word that we can use to mean "positive or zero". John Conway
Wed, 29 Oct 2003 21:36:25 -0500 (EST) John Conway <conway@Math.Princeton.EDU> What we ought to do, is find an existing word that we can use to mean "positive or zero". Is nonnegative (or non-negative) too ugly?
On Wed, 29 Oct 2003, Michael B Greenwald wrote:
Wed, 29 Oct 2003 21:36:25 -0500 (EST) John Conway <conway@Math.Princeton.EDU>
What we ought to do, is find an existing word that we can use to mean "positive or zero".
Is nonnegative (or non-negative) too ugly?
Well, yes, but that's not its worst defect. Two worse ones are that it defines a positive property as the negative of a negative one (ugh!), and that it doesn't work for general partial orders, for which "greater than or equals" doesn't mean the same as "not less than". What we need is a single word (behaving like "over") for the simple concet ">=", which would allow "over-zero" to substitute for the present "non-negative". John Conway
Perhaps `Peano number' ??? R. On Wed, 29 Oct 2003, John Conway wrote:
On Wed, 29 Oct 2003, Michael B Greenwald wrote:
Wed, 29 Oct 2003 21:36:25 -0500 (EST) John Conway <conway@Math.Princeton.EDU>
What we ought to do, is find an existing word that we can use to mean "positive or zero".
Is nonnegative (or non-negative) too ugly?
Well, yes, but that's not its worst defect. Two worse ones are that it defines a positive property as the negative of a negative one (ugh!), and that it doesn't work for general partial orders, for which "greater than or equals" doesn't mean the same as "not less than".
What we need is a single word (behaving like "over") for the simple concet ">=", which would allow "over-zero" to substitute for the present "non-negative".
John Conway
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On Thu, 30 Oct 2003, Richard Guy wrote:
Perhaps `Peano number' ??? R.
No, because I want to use it also for non-negative reals, etc. Something abbreviating "at-least-zero" is what I mean. Actually, if we could just get "at-least" down to one short enough word, that would be good enough, since we could say "[word]-zero". You might also like to think along the lines of "zero-or-more". Newly-invented words like "zops and zons" are wonderful in theory, but will never catch on. JHC
How about "from-zero"?
Date: Fri, 31 Oct 2003 13:33:03 -0500 (EST) From: John Conway <conway@Math.Princeton.EDU> X-BeenThere: math-fun@mailman.xmission.com X-Mailman-Version: 2.1.1 Precedence: list Reply-To: math-fun <math-fun@mailman.xmission.com> List-Id: math-fun <math-fun.mailman.xmission.com> List-Help: <mailto:math-fun-request@mailman.xmission.com?subject=help> List-Post: <mailto:math-fun@mailman.xmission.com> List-Subscribe: <http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun>, <mailto:math-fun-request@mailman.xmission.com?subject=subscribe> List-Archive: <http://mailman.xmission.com/cgi-bin/mailman/private/math-fun> List-Unsubscribe: <http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun>, <mailto:math-fun-request@mailman.xmission.com?subject=unsubscribe> X-Spam-Checker-Version: SpamAssassin 2.60-csdcf (1.212-2003-09-23-exp) on cs3.Stanford.EDU X-Spam-Level: X-Spam-Status: No, hits=-4.8 required=7.0 tests=AWL,BAYES_00 autolearn=ham version=2.60-csdcf
On Thu, 30 Oct 2003, Richard Guy wrote:
Perhaps `Peano number' ??? R.
No, because I want to use it also for non-negative reals, etc.
Something abbreviating "at-least-zero" is what I mean.
Actually, if we could just get "at-least" down to one short enough word, that would be good enough, since we could say "[word]-zero".
You might also like to think along the lines of "zero-or-more".
Newly-invented words like "zops and zons" are wonderful in theory, but will never catch on.
JHC
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What about "zog?" It's short and not already taken, so not ambiguous. It's also easy to spell! (Another possibility would be "zop.") Steve Gray ----- Original Message ----- From: "Michael B Greenwald" <mbgreen@central.cis.upenn.edu> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Wednesday, October 29, 2003 7:00 PM Subject: Re: [math-fun] Simple EF
Wed, 29 Oct 2003 21:36:25 -0500 (EST) John Conway <conway@Math.Princeton.EDU>
What we ought to do, is find an existing word that we can use to mean "positive or zero".
Is nonnegative (or non-negative) too ugly?
At 03:35 AM 10/31/03 -0800, you wrote:
What about "zog?" It's short and not already taken, so not ambiguous. It's also easy to spell!
You probably don't want to know that ZOG is an acronym used by antisemitic conspiracy theorists; it stands for Zionist Occupied Government, and refers to the theory that at some point in the past there was a Bad Event and ever since then the USA has been secretly run by Jews.
(Another possibility would be "zop.")
As far as I know, "zop" is not so embarrassingly taken already. I was also thinking maybe we could use "count" as a noun. That is, 0 is a count, 1 is a count, but -1 isn't a count. "Tale" is also possible etymologically, since "tell" used to be synonymous with "count"; near the beginning of Hamlet some character explains that the ghost hung around "while one with moderate haste might tell a hundred". I rather like the idea that every nonnegative integer is a "tale". -A
I didn't know about "ZOG." Let me instead suggest "zom," in addition to zop. A completely new word is less likely to result in confusion, I think, than tale or count. Zop and zom don't need "a" in front, so you can say "if x is zop," etc. I wonder what the editor will think if I use it in my next paper? ----- Original Message ----- From: "Allan C. Wechsler" <acw@alum.mit.edu> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Thursday, October 30, 2003 6:45 PM Subject: Re: [math-fun] Simple EF
At 03:35 AM 10/31/03 -0800, you wrote:
What about "zog?" It's short and not already taken, so not ambiguous. It's also easy to spell!
You probably don't want to know that ZOG is an acronym used by antisemitic conspiracy theorists; it stands for Zionist Occupied Government, and refers to the theory that at some point in the past there was a Bad Event and ever since then the USA has been secretly run by Jews.
(Another possibility would be "zop.")
As far as I know, "zop" is not so embarrassingly taken already.
I was also thinking maybe we could use "count" as a noun. That is, 0 is a count, 1 is a count, but -1 isn't a count. "Tale" is also possible etymologically, since "tell" used to be synonymous with "count"; near the beginning of Hamlet some character explains that the ghost hung around "while one with moderate haste might tell a hundred". I rather like the idea that every nonnegative integer is a "tale". -A
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Whatever happened to |N, as in "Natural" numbers? Call it a "natural". Computer languages such as Ada have had to deal with this same problem -- that of naming the set of non-negative numbers. I think that C/C++ call these "unsigned ints", or unsigned's, for short. At 11:32 AM 10/31/03 -0800, Steve Gray wrote:
I didn't know about "ZOG." Let me instead suggest "zom," in addition to zop. A completely new word is less likely to result in confusion, I think, than tale or count. Zop and zom don't need "a" in front, so you can say "if x is zop," etc. I wonder what the editor will think if I use it in my next paper?
----- Original Message ----- From: "Allan C. Wechsler" <acw@alum.mit.edu> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Thursday, October 30, 2003 6:45 PM Subject: Re: [math-fun] Simple EF
At 03:35 AM 10/31/03 -0800, you wrote:
What about "zog?" It's short and not already taken, so not ambiguous. It's also easy to spell!
You probably don't want to know that ZOG is an acronym used by antisemitic conspiracy theorists; it stands for Zionist Occupied Government, and refers to the theory that at some point in the past there was a Bad Event and ever since then the USA has been secretly run by Jews.
(Another possibility would be "zop.")
As far as I know, "zop" is not so embarrassingly taken already.
I was also thinking maybe we could use "count" as a noun. That is, 0 is a count, 1 is a count, but -1 isn't a count. "Tale" is also possible etymologically, since "tell" used to be synonymous with "count"; near the beginning of Hamlet some character explains that the ghost hung around "while one with moderate haste might tell a hundred". I rather like the idea that every nonnegative integer is a "tale". -A
On Fri, 31 Oct 2003, Henry Baker wrote:
Whatever happened to |N, as in "Natural" numbers? Call it a "natural".
There are two objections to this. The first is that my request was for a word meaning "at least zero". This won't be applied only to integers. The second is that there are still two schools of thought about "natural number", the "inclusivists" (like me) who count 0 as one, and the "exclusivists" who don't. Until the great day when the inclusivists win, it remains ambiguous.
Computer languages such as Ada have had to deal with this same problem -- that of naming the set of non-negative numbers.
I think that C/C++ call these "unsigned ints", or unsigned's, for short.
Those are slightly different again, since the "unsigned integer 5" is really the quotient concept {5, -5} rather than the sub-concept +5. John Conway
participants (9)
-
Alec Mihailovs -
Allan C. Wechsler -
Andy Latto -
Henry Baker -
John Conway -
John McCarthy -
Michael B Greenwald -
Richard Guy -
Steve Gray