| T.R | Title | User | Personal
Name | Date | Lines |
|---|
| 1280.1 | | HPSTEK::XIA | In my beginning is my end. | Tue Aug 07 1990 00:39 | 11 |
| re .0,
Franklin,
0
If I remember correctly 0 is treated as undefined (in high school that
is), but I guess you can extend the definition of exponential to
include that. As to what is the most natural extention, I would define
it as 1.
Eugene
|
| 1280.2 | 1 | HERON::BUCHANAN | combinatorial bomb squad | Tue Aug 07 1990 06:35 | 7 |
| The number of different functions from a set of cardinality X to
a set of cardinality Y is Y^X. If X = 0, then there will be precisely 1
function from X to Y, irrespective of the size of Y, ie: even if Y = 0. So to
define 0^0 = 1 is consistent with this common usage.
Regards,
Andrew.
|
| 1280.3 | Anything divided by itself equals 1... | EEMELI::TFORSELL | EarlyWormGetsCaughtByEarlyBird! | Tue Aug 07 1990 11:25 | 16 |
| Mathematically, might be something like this:
m=n <=> m-n=0
m m
0 m-m x 0 m-n x
x = x = -- = 1 OR x = x = -- = 1
m (whichever n
x one prefers) x
Though there is actually a division by zero if x=0, but we have to
live with that ;-)
Rgrds,
Toffe
|
| 1280.4 | discussed previously | EAGLE1::BEST | R D Best, sys arch, I/O | Tue Aug 07 1990 12:29 | 6 |
| This question has been discussed at length elsewhere in this notesfile.
I think the previous conclusion was that it can be defined several ways,
none of which are more meaningful than other ways.
Previous consensus was that a program should evaluate this to 'undefined'.
It's a little difficult to imagine where this might arise in practice.
|
| 1280.5 | | GUESS::DERAMO | Dan D'Eramo | Tue Aug 07 1990 12:58 | 11 |
| This question has been discussed at length elsewhere in this notesfile.
I think the previous conclusion was that it can be defined several ways,
none of which are more meaningful than other ways.
Oh no. An answer of 1 is definitely more meaningful than
any other way. The answer is one when you treat it as
cardinal exponentiation, and the answer is one when you
treat it as iterating a binary operation that has an
identity element.
Dan
|
| 1280.6 | | TRACE::GILBERT | Ownership Obligates | Tue Aug 07 1990 13:10 | 10 |
| > Oh no. An answer of 1 is definitely more meaningful than
> any other way. The answer is one when you treat it as
Well, we can make a fair case for 0, too.
lim x^0 = 1 lim 0^x = 0
x->0 x->0
lim x^x = 1
x->0
|
| 1280.7 | | GUESS::DERAMO | Dan D'Eramo | Tue Aug 07 1990 14:15 | 5 |
| A fair case, perhaps, but even your own reply gives twice
as much evidence for 0^0 = 1, which is only natural as
a much stronger case can be made for that answer.
Dan
|
| 1280.8 | | HERON::BUCHANAN | combinatorial bomb squad | Tue Aug 07 1990 15:01 | 4 |
| As Peter suggests note 610 treats this little problem.
Cheers,
Andrew.
|
| 1280.9 | | TRACE::GILBERT | Ownership Obligates | Fri Aug 10 1990 10:57 | 1 |
| Sorry, Andrew. It was Dan (in .5) with the good memory.
|
| 1280.10 | though I do have a good memory! :-) | GUESS::DERAMO | Dan D'Eramo | Fri Aug 10 1990 11:19 | 13 |
| >> Sorry, Andrew. It was Dan (in .5) with the good memory.
No ... the top, unindented part of .5 was quoting from .4,
and the bottom, indented part was my reply. The person
who said
"This question has been discussed at length elsewhere in this notesfile."
was
EAGLE1::BEST "R D Best, sys arch, I/O"
Dan
|
| 1280.11 | something out of nothing ?? | SMAUG::ABBASI | | Fri Aug 10 1990 15:23 | 6 |
|
0
0 = 1 is against the principle of conversation of energy, which
indicates that you cant get something out of nothing !
/naser
|
| 1280.12 | | HPSTEK::XIA | In my beginning is my end. | Fri Aug 10 1990 15:57 | 5 |
| re .11,
What are you talking about?
Eugene
|
| 1280.13 | 0**0 = 1 <=> bing bang theory | SMAUG::ABBASI | | Thu Aug 16 1990 17:20 | 5 |
| I guess I was trying to relate that formula to something in physical
world where you dont get something from nothing.
I imaging '0' as nothing and '1' as "something"
but this is mathematics and so I'll shutup..
|
| 1280.14 | (0^0) = (o^o) + \00/ ;-) | UKEDU::HARMER | Geoff Harmer U.K. Edu (830) 6229 | Tue Aug 21 1990 17:46 | 1 |
|
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