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| SolomonGrundy |
 Posted: Sat Jan 19, 2008 4:29 pm Post subject: 0 * 0 = ? |
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Wht is 0 * 0 and what results is giving to you all?
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Solomon Grundy
In 1944, this creature rose from the swamp, with tremendous strength and some dormant memories that for example allowed him to speak English, but not knowing what he was, and not remembering Cyrus Gold or his fate. Wandering throughout the swamp, he encountered two escaped criminals, killed them, and took their clothes. When they asked him his name, he simply muttered that he had been born on Monday. Reminded of an old nursery rhyme about a man born on Monday, the thugs named the creature "Solomon Grundy". |
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| Chemboy |
| Posted: Sat Jan 19, 2008 7:45 pm Post subject: Re: 0 * 0 = ? |
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| SolomonGrundy wrote: |
| Wht is 0 * 0 and what results is giving to you all? |
Zero times zero is zero. Multiplication can be looked at as an iteration of the addition operator. Zero times zero means you're adding zero to itself zero times, yielding zero. Why do you ask?
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| SolomonGrundy |
| Posted: Sat Jan 19, 2008 8:13 pm Post subject: |
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And 0 : 0 is 0 i see ... How can 0 be addaed and multyply or put in an equation to become 1?
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Solomon Grundy
In 1944, this creature rose from the swamp, with tremendous strength and some dormant memories that for example allowed him to speak English, but not knowing what he was, and not remembering Cyrus Gold or his fate. Wandering throughout the swamp, he encountered two escaped criminals, killed them, and took their clothes. When they asked him his name, he simply muttered that he had been born on Monday. Reminded of an old nursery rhyme about a man born on Monday, the thugs named the creature "Solomon Grundy". |
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| serpicojr |
| Posted: Sat Jan 19, 2008 11:43 pm Post subject: |
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If by 0:0 you mean 0/0, i.e. 0 divided by 0, then no, 0:0 ≠ 0. Division by 0 doesn't make sense, in fact. Division is supposed to be the inverse of the multiplication operator. In mathematical terms, we have that:
a:b = c
means the same thing as:
a = bc
and we want b to be uniquely determined by a and c. The expression a:0 for a ≠ 0 makes no sense, as otherwise we would have a = 0c = 0. And the expression 0:0 makes no sense, as 0 = 0c for any value of c.
This may seem like a flaw of our number system; it may seem like we should be able to define 0:0 or 1:0. But we shouldn't. In fact, it's pretty essential to mathematics for these expressions to not make sense. |
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| Guest |
| Posted: Sun Jan 20, 2008 4:17 am Post subject: |
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| 1 divided by zero to me means there is nothing to divide by therefore there simply is no answer, with nothing to divide by, no action can take place thus no result can bo obtained. Same for multiply. |
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| serpicojr |
| Posted: Sun Jan 20, 2008 9:12 am Post subject: |
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| You're suggesting multiplication by 0 shouldn't be meaningful? |
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| accountabled |
| Posted: Sun Jan 20, 2008 11:02 am Post subject: |
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A while ago I've tried to construct a kind of 'nulliair' mathematics.
My thought process was as follows:
There's a subtle difference between the divisions 0/0 and 1/0. The first is 'undetermined' and the latter is "undefined". You might reason that 0 x 0 = 0 and therefore 0 / 0=0, but there's clearly no definable solution like 1/0 = 0 since 0 x 0 is not equal to 1.
As an analogy to i^2 = -1, I then just tried to define 1/0 as follows:
j = 1 / 0 --> 0j = 1 --> 1/j = 0
And produced the following calculation rules:
Addition:
- aj + bj = (a + b) j for all a<>0 and b<>0
- aj + bj = 1 + bj for a=0, b <> 0
- aj + bj = aj + 1 for b=0, a <> 0
- aj + bj = 2 for a=0 and b=0
Subtraction:
- aj – bj = (a - b) j for all a<>0 en b<>0 and a<>b
- aj – bj = 0j = 1 for all a=b
- aj – bj = 1 - bj for a=0, b <> 0
- aj – bj = aj - 1 for b=0, a <> 0
- aj – bj = 1 - 1 = 0 for a=0 en b=0
Division:
- aj / bj = (aj * 1/j) * 1/b = (aj * 0) * 1/b = 1/b for all a<>0 and b<>0
- aj / bj = (aj * 1/j) * 1/b = (0j * 0) * 1/b = 0 for a=0, b <> 0
- aj / bj = (aj * 1/j) * 1/b = (aj * 0) * 1/0 = j for b=0, a <> 0
- aj / bj = (aj * 1/j) * 1/b = (0j * 0) * 1/0 = 1 for a=0 and b=0
Multiplication:
- aj * bj = (a*b)j^2 for all a<>0 and b<>0
- aj * bj = bj for all a=0, b <>0
- aj * bj = aj for all b=0, a <> 0
- aj * bj = 1 for all a=0 and b=0
Powers:
(j^a):
- j^a * j^b = j ^(a+b) for all (a+b)>0
- j^a * j^b = 1 for all (a+b) = 0 (a=-b or (a=0 and b=0))
- j^a *j^b = 1/j^(a+b) for all (a+b) < 0
- j^a / j^b = j ^(a-b) for all (a-b)>0
- j^a / j^b = 1 for all (a-b) = 0 (a=b or (a=0 and b=0))
- j^a / j^b = 1/j^(a-b) for all (a-b) < 0
(a^j):
- a^bj * a^cj = a ^ ((b+c)j) for all (b+c) <>0
- a^bj * a^cj = a for all (b+c) = 0
- a^bj / a^cj = a ^((b-c)j) for all (b-c) <>0
- a^bj / a^cj = 1 for all (b-c) = 0
Goniometric:
- tan (90 + n*180) = j (n = 0, 1, 2, ...)
- sin (90 + n * 180) = j * cos (90 + n * 180)
- cotan (90 + n*180) = 1/j = 0
Commutative?
For all a and b it's true that:
- aj + bj = bj + aj
- 2j + 0j = 0j + 2j (= 1 + 2j)
- aj * bj = bj * aj
- 1j * 2j = 2j * 1j (= 2j^2)
Distributive over addition? (hold your breath till the end Serpicojr!  )
For all a, b and c it's true that:
- (aj + bj) * cj = aj * cj + bj * cj.
- (0j + 0j) * 0j = 1*1 + 1*1 (= 2)
- (1j + 1j) * 1j = 1j*1j + 1j*1j (= 2j^2)
- (0j + 1j) * 0j = 0j * 0j + 1j * 0j (= 1 + j)
Associative?
For all a, b and b it's true that:
- aj + (bj + cj) = (aj + bj) + cj
- 0j * (1j * 2j) = (0j * 1j) * 2j (= 2j^2)
- aj * (bj * cj) = (aj * bj) * cj
- 0j * (1j * 2j) = (0j * 1j) * 2j (= 2j^2)
- 2j * (3j * 4j) = (2j * 3j) * 4j (= 24j^3)
I've even plotted the first ever 'nulliair plane' (with the imaginairy axis cutting the real axis in 1).
Of course the main problem is in the 'distribution over addition' where (0+0) j = 0j + 0j = 1 + 1 = 2 but also 0j = 1. So: 1=2 or any number you'd like...
I've never found a way to solve this problem other than making surreal assumptions like:
1. accepting that in the nulliair world it's just true that 1=2, 1=3 ... 1=n
2. assuming that (a + b) j is only "distributive over addition" for a<>0 and b <> 0. In the special case that a=0 and b=0 then (a +/- b) is always equal to 0j.
3. making all zero's unique in the nulliair world and assigning special properties to them.
4. dropping the whole idea...  |
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| Guest |
| Posted: Sun Jan 20, 2008 11:13 am Post subject: |
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| Hmmm confusing your using 'j' as to engineers it is the square root of -1 |
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| serpicojr |
| Posted: Sun Jan 20, 2008 11:59 am Post subject: |
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I think you've hit the problem on the head. If you want lots of properties to hold true, you're going to get "nonsense" statements like 0 = 1. This is fine and dandy if you don't care about doing usual arithmetic in your new number system. But I have a feeling that you do. So... you have to drop some properties. Arithmetic with j can't satisfy all the properties you might hope it does. Evidently, the problem is with this argument:
1 = 0j = (0+0)j = 0j+0j = 1+1 = 2
What did you we here? Two things: 1 = 0j and distribution over multiplication by j. So you have to give up one of those guys. You want 1 = 0j. So you have to get rid of distribution over multiplication by j. I don't think this gets you off the hook, though--you've included a lot of properties, and so there's a lot of potential for inconsistency. In any case, things are getting kind of complicated, and arithmetic operations should aim to be simple (in my world anyway). At the end of the day, I would just give up on trying to divide by 0.
I recall looking at something recently (year or two ago?) where some guy made up rules for arithmetic that included division by 0, plus and minus infinity, and one extra number representing "undefined". Basically, any time he tried to define an operation that necessarily led to an inconsistency, he let the result be undefined, and any operation involving undefined resulted in undefined. But this is kind of a cop out and is no more useful than just saying that an expression is undefined.
Let me also add that a lot of mathematical subjects have very good ways of dealing with the notion of division by 0--complex function theory, for example. I could discuss this at greater length. |
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| accountabled |
| Posted: Sun Jan 20, 2008 12:29 pm Post subject: |
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Posts: 35
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| Quote: |
| Recall looking at something recently (year or two ago?) where some guy made up rules for arithmetic that included division by 0, plus and minus infinity, and one extra number representing "undefined". |
Think I found the guy that you mentioned.
http://www.badscience.net/?p=335
His theory was as follows:
1/0 = inifinity
-1/0 = -infinity
0/0 = NaN (Not a Number) let's call it @
He then uses the following logic to solve a '1200 year old problem' of 0^0:
0^0
= 0^(1-1)
= 0^1 * 0^(-1)
= (0/1)^1 * (0/1)^(-1)
= 0/1 * 1/0
= 0/0
= @
| Quote: |
| Let me also add that a lot of mathematical subjects have very good ways of dealing with the notion of division by 0--complex function theory, for example. |
I've read about the Riemann Spheres and also about 'wheels'. Is that what you're referring to? |
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| serpicojr |
| Posted: Sun Jan 20, 2008 12:46 pm Post subject: |
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Yes, yes, and yes!
That's precisely the guy I was talking about. To be honest, the mathematics community isn't impressed by his work. I mean, it's all valid, and he clearly knows math, but there's a question about the importance of the work. It's a fine intellectual exercise to go through, but it's not going to cure cancer or prove the Riemann hypothesis.
The Riemann sphere is indeed an object which allows you to talk about functions which take on the value infinity (which is really the same thing as dividing by 0 in this scenario).
Actually, I wasn't really talking about wheels, but wheels are another solution to the problem of dividing by 0. I haven't really seen them used much, but that doesn't mean there's not some research group out there diligently working out wheel theory. If you want an algebraic/arithmetic/nonanalytic/nongeometric approach to dividing by 0, I'd say this is the way to go. |
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| accountabled |
| Posted: Sun Jan 20, 2008 1:01 pm Post subject: |
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| Quote: |
| I mean, it's all valid, and he clearly knows math, but there's a question about the importance of the work. It's a fine intellectual exercise to go through, but it's not going to cure cancer or prove the Riemann hypothesis. |
Just read his paper (it's in pdf on his site) and the idea of trying to avoid a 'division by zero' error in computersofware by constructing an elegant set of new rules, could have some practical use.
Dr James Anderson, from the University of Reading’s computer science department, says his new theorem solves an extremely important problem - the problem of nothing. “Imagine you’re landing on an aeroplane and the automatic pilot’s working,” he suggests. “If it divides by zero and the computer stops working - you’re in big trouble. If your heart pacemaker divides by zero, you’re dead.”
This is a famous real life example:
On September 21, 1997, a divide by zero error in the USS Yorktown (CG48) Remote Data Base Manager brought down all the machines on the network, causing the ship's propulsion system to fail. |
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| SolomonGrundy |
| Posted: Sun Jan 20, 2008 3:13 pm Post subject: |
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cosine of 0 is 1 right ?
sin 0 = 0: cos 0 = 1
why is that so?
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Solomon Grundy
In 1944, this creature rose from the swamp, with tremendous strength and some dormant memories that for example allowed him to speak English, but not knowing what he was, and not remembering Cyrus Gold or his fate. Wandering throughout the swamp, he encountered two escaped criminals, killed them, and took their clothes. When they asked him his name, he simply muttered that he had been born on Monday. Reminded of an old nursery rhyme about a man born on Monday, the thugs named the creature "Solomon Grundy". |
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| serpicojr |
| Posted: Sun Jan 20, 2008 3:33 pm Post subject: |
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| accountabled wrote: |
Just read his paper (it's in pdf on his site) and the idea of trying to avoid a 'division by zero' error in computersofware by constructing an elegant set of new rules, could have some practical use.
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True, avoiding these sorts of mistakes is worthwhile. I don't know and would be surprised if his solution was the first to this problem, though. And you don't need a new number system to accomplish this--you can just design your programs not to crash if division by zero is attempted.
| SolomonGrundy wrote: |
cosine of 0 is 1 right ?
sin 0 = 0: cos 0 = 1
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True indeed. |
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| SolomonGrundy |
| Posted: Sun Jan 20, 2008 3:38 pm Post subject: |
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so if cos 0 =1 then the solution to 0:0 is in the middle no?
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Solomon Grundy
In 1944, this creature rose from the swamp, with tremendous strength and some dormant memories that for example allowed him to speak English, but not knowing what he was, and not remembering Cyrus Gold or his fate. Wandering throughout the swamp, he encountered two escaped criminals, killed them, and took their clothes. When they asked him his name, he simply muttered that he had been born on Monday. Reminded of an old nursery rhyme about a man born on Monday, the thugs named the creature "Solomon Grundy". |
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