[math-fun] Is zero “weakly positive”?
f(x)=ax is strictly increasing iff a>0 and weakly increasing iff a >= 0, and we sometimes say that a is strictly positive as a way of saying a>0, so shouldn’t we say a is weakly positive iff a>=0? Does anyone use the phrase “weakly positive” in this way? Jim Propp
I've always heard "nonnegative" used for this concept. One word, four syllables, and meaning is immediately obvious even if you've never heard the word before. Better than two words, five syllables, and unfamiliar. Andy On Fri, Jul 27, 2018 at 12:53 AM, James Propp <jamespropp@gmail.com> wrote:
f(x)=ax is strictly increasing iff a>0 and weakly increasing iff a >= 0, and we sometimes say that a is strictly positive as a way of saying a>0, so shouldn’t we say a is weakly positive iff a>=0?
Does anyone use the phrase “weakly positive” in this way?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Andy.Latto@pobox.com
Yes, nonnegative is the standard term for this, but I disagree that its meaning is immediately obvious to non-mathematicians: even some intelligent laypeople don’t realize you can take the word apart and deduce its meaning (a nonnegative number is a number that is not negative), while others confuse “not negative” with “positive”. Jim On Friday, July 27, 2018, Andy Latto <andy.latto@pobox.com> wrote:
I've always heard "nonnegative" used for this concept. One word, four syllables, and meaning is immediately obvious even if you've never heard the word before. Better than two words, five syllables, and unfamiliar.
Andy
On Fri, Jul 27, 2018 at 12:53 AM, James Propp <jamespropp@gmail.com> wrote:
f(x)=ax is strictly increasing iff a>0 and weakly increasing iff a >= 0, and we sometimes say that a is strictly positive as a way of saying a>0, so shouldn’t we say a is weakly positive iff a>=0?
Does anyone use the phrase “weakly positive” in this way?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Andy.Latto@pobox.com
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So your intent is that "weakly positive" be a synonym for "nonnegative" that is more perspicuous to non-mathematicians? I think it will not serve. On Fri, Jul 27, 2018 at 8:24 AM, James Propp <jamespropp@gmail.com> wrote:
Yes, nonnegative is the standard term for this, but I disagree that its meaning is immediately obvious to non-mathematicians: even some intelligent laypeople don’t realize you can take the word apart and deduce its meaning (a nonnegative number is a number that is not negative), while others confuse “not negative” with “positive”.
Jim
On Friday, July 27, 2018, Andy Latto <andy.latto@pobox.com> wrote:
I've always heard "nonnegative" used for this concept. One word, four syllables, and meaning is immediately obvious even if you've never heard the word before. Better than two words, five syllables, and unfamiliar.
Andy
On Fri, Jul 27, 2018 at 12:53 AM, James Propp <jamespropp@gmail.com> wrote:
f(x)=ax is strictly increasing iff a>0 and weakly increasing iff a >= 0, and we sometimes say that a is strictly positive as a way of saying a>0, so shouldn’t we say a is weakly positive iff a>=0?
Does anyone use the phrase “weakly positive” in this way?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Andy.Latto@pobox.com
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If I remember correctly into the dim past, in high school positive or negative sometimes included zero, sometimes didn’t. I was introduced to “nonnegative” in college where it mattered more. “Weakly positive” reminds me of “weakly monotonic” for functions, and my experience with teaching too many Calculus I classes is that college students get it more easily when it is explicitly stated as “derivative positive or zero” or “derivative negative or zero.” My experience suggests that anyone not trained up to calculus will not be familiar with using the word weakly in this context, and will need an additional definition. I would prefer to stick to non-negative or use “x greater than or equal to zero” which is clear to anyone having done any algebra in middle or high school. Steve On Jul 27, 2018, at 8:58 AM, Allan Wechsler <acwacw@gmail.com<mailto:acwacw@gmail.com>> wrote: So your intent is that "weakly positive" be a synonym for "nonnegative" that is more perspicuous to non-mathematicians? I think it will not serve. On Fri, Jul 27, 2018 at 8:24 AM, James Propp <jamespropp@gmail.com<mailto:jamespropp@gmail.com>> wrote: Yes, nonnegative is the standard term for this, but I disagree that its meaning is immediately obvious to non-mathematicians: even some intelligent laypeople don’t realize you can take the word apart and deduce its meaning (a nonnegative number is a number that is not negative), while others confuse “not negative” with “positive”. Jim On Friday, July 27, 2018, Andy Latto <andy.latto@pobox.com<mailto:andy.latto@pobox.com>> wrote: I've always heard "nonnegative" used for this concept. One word, four syllables, and meaning is immediately obvious even if you've never heard the word before. Better than two words, five syllables, and unfamiliar. Andy On Fri, Jul 27, 2018 at 12:53 AM, James Propp <jamespropp@gmail.com<mailto:jamespropp@gmail.com>> wrote: f(x)=ax is strictly increasing iff a>0 and weakly increasing iff a >= 0, and we sometimes say that a is strictly positive as a way of saying a>0, so shouldn’t we say a is weakly positive iff a>=0? Does anyone use the phrase “weakly positive” in this way? Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com<mailto:math-fun@mailman.xmission.com> https://urldefense.proofpoint.com/v2/url?u=https-3A__mailman.xmission.com_cg... -- Andy.Latto@pobox.com<mailto:Andy.Latto@pobox.com> _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com<mailto:math-fun@mailman.xmission.com> https://urldefense.proofpoint.com/v2/url?u=https-3A__mailman.xmission.com_cg... _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com<mailto:math-fun@mailman.xmission.com> https://urldefense.proofpoint.com/v2/url?u=https-3A__mailman.xmission.com_cg... _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com<mailto:math-fun@mailman.xmission.com> https://urldefense.proofpoint.com/v2/url?u=https-3A__mailman.xmission.com_cg...
I agree with Allan 100%; I didn't mean to suggest that "weakly positive" would be any clearer. Jim On Fri, Jul 27, 2018 at 8:58 AM, Allan Wechsler <acwacw@gmail.com> wrote:
So your intent is that "weakly positive" be a synonym for "nonnegative" that is more perspicuous to non-mathematicians? I think it will not serve.
On Fri, Jul 27, 2018 at 8:24 AM, James Propp <jamespropp@gmail.com> wrote:
Yes, nonnegative is the standard term for this, but I disagree that its meaning is immediately obvious to non-mathematicians: even some intelligent laypeople don’t realize you can take the word apart and deduce its meaning (a nonnegative number is a number that is not negative), while others confuse “not negative” with “positive”.
Jim
On Friday, July 27, 2018, Andy Latto <andy.latto@pobox.com> wrote:
I've always heard "nonnegative" used for this concept. One word, four syllables, and meaning is immediately obvious even if you've never heard the word before. Better than two words, five syllables, and unfamiliar.
Andy
On Fri, Jul 27, 2018 at 12:53 AM, James Propp <jamespropp@gmail.com> wrote:
f(x)=ax is strictly increasing iff a>0 and weakly increasing iff a >= 0, and we sometimes say that a is strictly positive as a way of saying a>0, so shouldn’t we say a is weakly positive iff a>=0?
Does anyone use the phrase “weakly positive” in this way?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Andy.Latto@pobox.com
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In French, "positive" includes 0, whereas in English, it excludes zero. "Nonnegative" was coined to clarify the distinction. A related pair of terms is "monotonically increasing" vs. "strictly increasing". On Fri, Jul 27, 2018 at 8:23 AM, James Propp <jamespropp@gmail.com> wrote:
I agree with Allan 100%; I didn't mean to suggest that "weakly positive" would be any clearer.
Jim
On Fri, Jul 27, 2018 at 8:58 AM, Allan Wechsler <acwacw@gmail.com> wrote:
So your intent is that "weakly positive" be a synonym for "nonnegative" that is more perspicuous to non-mathematicians? I think it will not serve.
On Fri, Jul 27, 2018 at 8:24 AM, James Propp <jamespropp@gmail.com> wrote:
Yes, nonnegative is the standard term for this, but I disagree that its meaning is immediately obvious to non-mathematicians: even some intelligent laypeople don’t realize you can take the word apart and deduce its meaning (a nonnegative number is a number that is not negative), while others confuse “not negative” with “positive”.
Jim
On Friday, July 27, 2018, Andy Latto <andy.latto@pobox.com> wrote:
I've always heard "nonnegative" used for this concept. One word, four syllables, and meaning is immediately obvious even if you've never heard the word before. Better than two words, five syllables, and unfamiliar.
Andy
On Fri, Jul 27, 2018 at 12:53 AM, James Propp <jamespropp@gmail.com> wrote:
f(x)=ax is strictly increasing iff a>0 and weakly increasing iff a >= 0, and we sometimes say that a is strictly positive as a way of saying a>0, so shouldn’t we say a is weakly positive iff a>=0?
Does anyone use the phrase “weakly positive” in this way?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Andy.Latto@pobox.com
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-- Mike Stay - metaweta@gmail.com http://www.math.ucr.edu/~mike http://reperiendi.wordpress.com
I commonly use "nondecreasing". Brent On 7/27/2018 12:20 PM, Mike Stay wrote:
In French, "positive" includes 0, whereas in English, it excludes zero. "Nonnegative" was coined to clarify the distinction. A related pair of terms is "monotonically increasing" vs. "strictly increasing".
On Fri, Jul 27, 2018 at 8:23 AM, James Propp <jamespropp@gmail.com> wrote:
I agree with Allan 100%; I didn't mean to suggest that "weakly positive" would be any clearer.
Jim
On Fri, Jul 27, 2018 at 8:58 AM, Allan Wechsler <acwacw@gmail.com> wrote:
So your intent is that "weakly positive" be a synonym for "nonnegative" that is more perspicuous to non-mathematicians? I think it will not serve.
On Fri, Jul 27, 2018 at 8:24 AM, James Propp <jamespropp@gmail.com> wrote:
Yes, nonnegative is the standard term for this, but I disagree that its meaning is immediately obvious to non-mathematicians: even some intelligent laypeople don’t realize you can take the word apart and deduce its meaning (a nonnegative number is a number that is not negative), while others confuse “not negative” with “positive”.
Jim
On Friday, July 27, 2018, Andy Latto <andy.latto@pobox.com> wrote:
I've always heard "nonnegative" used for this concept. One word, four syllables, and meaning is immediately obvious even if you've never heard the word before. Better than two words, five syllables, and unfamiliar.
Andy
On Fri, Jul 27, 2018 at 12:53 AM, James Propp <jamespropp@gmail.com> wrote:
f(x)=ax is strictly increasing iff a>0 and weakly increasing iff a >= 0, and we sometimes say that a is strictly positive as a way of saying a>0, so shouldn’t we say a is weakly positive iff a>=0?
Does anyone use the phrase “weakly positive” in this way?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Andy.Latto@pobox.com
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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When my checking account falls below $100, it's weakly positive. I vote for "nonnegative". Brent On 7/27/2018 5:24 AM, James Propp wrote:
Yes, nonnegative is the standard term for this, but I disagree that its meaning is immediately obvious to non-mathematicians: even some intelligent laypeople don’t realize you can take the word apart and deduce its meaning (a nonnegative number is a number that is not negative), while others confuse “not negative” with “positive”.
Jim
On Friday, July 27, 2018, Andy Latto <andy.latto@pobox.com> wrote:
I've always heard "nonnegative" used for this concept. One word, four syllables, and meaning is immediately obvious even if you've never heard the word before. Better than two words, five syllables, and unfamiliar.
Andy
On Fri, Jul 27, 2018 at 12:53 AM, James Propp <jamespropp@gmail.com> wrote:
f(x)=ax is strictly increasing iff a>0 and weakly increasing iff a >= 0, and we sometimes say that a is strictly positive as a way of saying a>0, so shouldn’t we say a is weakly positive iff a>=0?
Does anyone use the phrase “weakly positive” in this way?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Andy.Latto@pobox.com
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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participants (6)
-
Allan Wechsler -
Andy Latto -
Brent Meeker -
James Propp -
Lucas, Stephen K - lucassk -
Mike Stay