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Author

Joined: 25 Sep 2003
Posts: 2141
Location: Estonia
Hey, I like apples

If I have two apples and need to share it with another person - we both get one (num/num=1). If now I have no apples and still need to share with somebody, we don't get anything and thats logical too (0/num=0).

It gets interesting when I don't have any apples and nobody wants them (0/0). I can say that per person you get an apple, but I can also promise that every person in this null set will get a million apples and I am correct. How would you measure the apple-count per person if you don't have anybody.

0/0 simply is undefined although lim tells us that 0/0 is closing on (nearing to?) 1 from either side.

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09 Mar 2008, 10:52
edfed

Joined: 20 Feb 2006
Posts: 4237
Location: 2018
edfed
0/0=0
0*0=0
0+0=0
0-0=0

zero or the magic number.

the return of zero. with tom hanks, bruce willis, anthony hopkins, matt damon, lucy liu, rocco sifredi, clara morgane and nathalie portman..

yey!

what is the probability that this film will exist one day?

P=0

the return of zero!
09 Mar 2008, 11:20
MCD

Joined: 21 Aug 2004
Posts: 604
Location: Germany
MCD
hmm, if the reciprocal of 0 were defined, then you actually could get to this:
Code:
`+âˆž = + (1/0) = 1/ (+0) = 1 / (-0) = - (1/0) = -âˆž    `

which doesn't make sense in many fields, but one interesting one might be the one used in Smith-Diagramms

One good reason why 0/0 is usually considered undefined is the following:
Code:
```    0 * any_number = 0
<=> any_number = 0 / 0
```

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MCD - the inevitable return of the Mad Computer Doggy

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14 Mar 2008, 05:15
Borsuc

Joined: 29 Dec 2005
Posts: 2466
Location: Bucharest, Romania
Borsuc
Hmm.. 1/+0 is not equal to 1/-0; they are pretty much very far away (from 0) both.

Actually, would it make more sense if we said that the function r(x) has two returning values when x=0? (let's say -oo and +oo)? (note i don't particularly support this idea).

r(x) is undefined at 0 because you do not know which of these two values to take -- but the ambiguity can be solved if we use the +0 and -0 notations (they simply mean "take the positive or negative, respectively").
17 Mar 2008, 12:45
Tomasz Grysztar
Assembly Artist

Joined: 16 Jun 2003
Posts: 7724
Location: Kraków, Poland
Tomasz Grysztar
On the projective line they are both the same point - and the line becomes a circle then.

 Description: You can easily map real line into circle this way. (It works also for the complex plane and the sphere). Filesize: 12.96 KB Viewed: 8763 Time(s)

17 Mar 2008, 13:19
sleepsleep

Joined: 05 Oct 2006
Posts: 8902
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sleepsleep
Quote:

Oddity 1:
0/number = 0
number/0 = undefined
number/number = 1
So what is 0/0

0 cake, divide by a number ~ resulted => 0. no division could perform, because no cake.
0/number = 0

5 slices of cake divided by 0 (person) = 5 slices of cake
no division could (perform), because cake consumed by nobody.
number/0 = number (according to my logic)

0 slices of cake divided by 0 human to consume = ill logic
why we want to divide empty with empty?

Last edited by sleepsleep on 23 Mar 2008, 00:01; edited 1 time in total
21 Mar 2008, 21:04
sleepsleep

Joined: 05 Oct 2006
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sleepsleep
if 0 means ZERO
for me, it means, whatever thing/algo that you associated with 0, will not and should not have any effect on the resulted calculation.
21 Mar 2008, 21:09
Borsuc

Joined: 29 Dec 2005
Posts: 2466
Location: Bucharest, Romania
Borsuc
Tomasz Grysztar wrote:
On the projective line they are both the same point - and the line becomes a circle then.
Cool representation -- I'm starting to think two's complement works similarly (you move counter-clockwise in the diagram, and infinity is the largest number you can hold in unsigned values, I mean, which becomes the largest negative number in signed values). That is why '-1' is so big (as an unsigned value).

sleepsleep wrote:
if 0 means ZERO
for me, it means, whatever thing/algo that you associated with 0, will not and should not have any effect on the resulted calculation.
So number*0 = number?
22 Mar 2008, 18:15
sleepsleep

Joined: 05 Oct 2006
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sleepsleep
Quote:

So number*0 = number?

3 * 2

* * *
* * *

3 cols and 2 rows, so we got 6 dots.
since i said, if 6 dots divide by 0, we have 6 dots still.
so 6 * 0 = 6,
6 * 1 = 6

6 * 0 = 6
Code:
```+-----------------+
|    *            |
|                 |
|  *              |
|        *        |
|  *              |
|              *  |
|           *     |
+-----------------+
```

6 dots exists, but no row been assigned to it, they scattered around like above ascii picture.

6 * 1 = 6
Code:
```+-----------------+
|                 |
|                 |
|  * * * * * *    |
|                 |
|                 |
|                 |
|                 |
+-----------------+
```
23 Mar 2008, 00:09
edfed

Joined: 20 Feb 2006
Posts: 4237
Location: 2018
edfed
forgot an essential detail.

0+0=0
then, 6*0 = 0
and in return, 6/0= oo
why?
simple, zero is nothing, how many nothing in somthing? an infinity.
then 6/0=oo and not 6
or at least 6/0= +32767 in 16 and 2^31-1 in 32bits
infinite depends on the resolution of the system, and is always the bigger value you can have.
in signed 16bitys, the maximum is 2^15-1, there are no value above this one.
23 Mar 2008, 00:16
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17279
revolution
Oddity 4:
• number*∞ = ∞
• number*0 = 0
So what is ∞*0 =
23 Mar 2008, 00:20
edfed

Joined: 20 Feb 2006
Posts: 4237
Location: 2018
edfed
∞*0 =0 because zero have the priority.
it's more frequent to cross zero than infinite.

and zero is sinonym of nothing, then, nothing*infinite = nothing.

zero can be interpreted as NO.
and NO is the total negation of something. then, NO * infinite = 0
23 Mar 2008, 00:22
sleepsleep

Joined: 05 Oct 2006
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sleepsleep
so i think i could introduce a new concept.

numbers exists in 2 form, scattered (S) and unscattered (US) form.

maybe we need to draft some rules for them
when S vs S, S vs US, US vs US
23 Mar 2008, 00:25
sleepsleep

Joined: 05 Oct 2006
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sleepsleep
Quote:

number*∞ = ∞

for me, i think
infinity is a concept, it is not a number.
u can't perform a number * infinity, because, infinity is a CONCEPT.
23 Mar 2008, 00:31
Jack

Joined: 16 Feb 2005
Posts: 21
Jack
sleepsleep, I think you are right.
try for example to picture in your mind an infinite universe, the mind can not comprehend something infinite, paradoxically you can not picture a finite universe, because you will think "what's beyond that"
23 Mar 2008, 22:36
AlexP

Joined: 14 Nov 2007
Posts: 561
Location: Out the window. Yes, that one.
AlexP
24 Mar 2008, 02:45
edfed

Joined: 20 Feb 2006
Posts: 4237
Location: 2018
edfed
it's both a gift, and a torture.
gift cause we have the power to think we are moer than skin, muscles and bones.

a torture cause we see we are only skin, muscles and bones.

you have the choise.
don't know, and be happy, but a bit stupid.
try to know, then, don't see any magic in the world, all have a logic explanation, then, no fantastic, just facts.

i'm in the second case, but more in the middle, try to know the maximum, don't know anything, be sad of my human condition, but feel happy to know there are billions light years to explore, and we cannot. no space ships to see the limit of our universe, and see that there is something different beyond the limits.

something so different that it cannot be part of our universe.

our universe is composed of vaccum, atoms, planets, suns, galaxies, galaxies clouds, etc...
waht can be the others things? that are not in our universe?

is it possible that imagination, in our brains, creats universe somewhere, in other dimensions.
24 Mar 2008, 13:38
MCD

Joined: 21 Aug 2004
Posts: 604
Location: Germany
MCD
Tomasz Grysztar wrote:
On the projective line they are both the same point - and the line becomes a circle then.

exactly this is the way the smith diagram can be defined and drawn.

I noted just another thing: while infinity is not an element of the real numbers, there are several uses of the set of the real numberes unified with positive and negative infinity, denoted as
Code:
```;tex
\R \cup \{-\infty, +\infty \}
```
02 Apr 2008, 13:10
LocoDelAssembly

Joined: 06 May 2005
Posts: 4633
Location: Argentina
LocoDelAssembly
I think this thread turned interesting to be kept in the unsafe Test Area, I'm moving it to Heap.
06 Apr 2008, 02:10
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17279
revolution
I give a small prize to the first person that can explain a simple method to convert 0.012345679(012345679) {parentheses meaning the nine digits are recurring} into 1/81, and can also generalise the method for any number, in any base, with any arbitrary recurring sequence after the decimal/binary/hex/whatever-base point.

The prize will be one star so don't be disappointed, okay
28 Sep 2008, 09:50
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