| T.R | Title | User | Personal
Name | Date | Lines |
|---|
| 1357.1 | | SHIRE::ALAIND | Alain Debecker @GEO DTN 821-4912 | Thu Dec 20 1990 15:55 | 37 |
| 1357.2 | | GUESS::DERAMO | Dan D'Eramo | Thu Dec 20 1990 17:38 | 11 |
| Someone on usenet noted that the definition also allowed
K to be the empty set or the singleton set containing
only the origin. In the latter case K = { su + tv : s, t >= 0 }
with u = v = (0,0).
re .-1
You twice use "positive" where I think you mean
"nonnegative", otherwise that looks right.
Dan
|
| 1357.3 | | SHIRE::ALAIND | Alain Debecker @GEO DTN 821-4912 | Fri Dec 21 1990 09:15 | 19 |
| > re .-2
>
> You twice use "positive" where I think you mean
> "nonnegative"
A matter of culture. In many countries, zero is taken as a
number both positive and negative, and the sentence "x is
smaller than y" means x <= y. In US and UK, zero is neither
positive nor negative, and "x is smaller than y" doesn't
allow for equality.
Nevertheless, you are right. I was lousy on the edges:
Note that the condition (4) is equivalent to the fact that
the cone is closed. An *open* set verifying condition (1)
to (3) is of the form K = { su + tv | s,t > 0 }. The same
demonstration holds: this time, the intersection of K and
the cone is open, thus of the form ]u,v[ instead of [u,v].
|
| 1357.4 | But this is English, right? | CHOVAX::YOUNG | Give peace a chance. | Fri Dec 21 1990 14:38 | 7 |
| Re .4:
But these are fairly precise terms in English. For instance,
"Positive" in English has a precise meaning, ie. "Greater than
zero."
-- Barry
|
| 1357.5 | Let he who is without sin(x) cast the first die | VMSDEV::HALLYB | The Smart Money was on Goliath | Fri Dec 21 1990 15:37 | 5 |
| Re: .4 [Re: .4 [Re: .4 [Re: .4 [Re: .4 [Re: .4 [ Re: .4 [Re: .4 [...
> But these are fairly precise terms in English. For instance,
As opposed to "unfairly precise"?
|
| 1357.6 | Precisely! | GUESS::DERAMO | Dan D'Eramo | Fri Dec 21 1990 16:55 | 5 |
| More like, as in "rather precise". More precise than
your usual English term, but not as precise as something
like "compact Hausdorff space".
Dan
|
| 1357.7 | A:x [Mathematician(x) -> Life_of_Nit_Picking(x)] | CHOVAX::YOUNG | Give peace a chance. | Fri Dec 21 1990 18:46 | 12 |
| Yeah, what Dan said.
Really though, my lousy spelling and usual fumble-fingered Notes
replies aside, when you discuss mathematics, you HAVE to be precise.
Mathematics more than any other field inherently relies on precise
terminology and precise statements.
What is, in polite conversation, merely a nit that only an irritating
pest would point out, in mathematical discussions can easily become a
pivotal issue or the fatal 'flaw' in a critical proof.
-- Barry
|
| 1357.8 | | SHIRE::ALAIND | Alain Debecker @GEO DTN 821-4912 | Fri Dec 28 1990 12:03 | 7 |
| Of course "positive" has a precise meaning in English, and I confess to
make a linguistic mish-mash from time to time. You know, just like when
you ask an Englishman why he is driving on the left side of the road and
he answers "because it is the right side".
Nevertheless in this precise case the demonstration was simpler with an
open cone.
|