Topic awaiting preservation: The Greatest Above All? Or not?

Can anyone give me the greatest number in the universe? No, it is not an infinite number, and Calvin and Hobbes numbers don't count (meaning eleventy-twelve). This number is a completely legitimate number.

---
"The Mystery of Life"
Vol. 841, Ch. 26
"All life begins with Nu and ends with Nu. This is the truth! This is my beleif! ...at least for now." - Chrono Trigger
><>

42.

But eleventy-twelve takes a very close second place.

"The score is still Q to 12!"

Ay no, I'm quite serious. There is a number that is greater than any number you can create.

And Raptor: 42 is the answer to the greatest question in life. This isn't the greatest question, just the greatest number

---
"The Mystery of Life"
Vol. 841, Ch. 26
"All life begins with Nu and ends with Nu. This is the truth! This is my beleif! ...at least for now." - Chrono Trigger
><>



[This message has been edited by Ruku (edited 09-12-2003).]

I guess perhaps 1 is the greatest number, because there is only 1 god, and god is the greatest. Blah. Blah Blah.
http://www.polarbearandco.com/Jinniyah.html

[This message has been edited by Gilbert Nolander (edited 09-12-2003).]

dangit wes, you beat me to it

chris


KAIROSinteractive

Ruku:

quote:

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There is a number that is greater than any number you can create.

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Yes its:

(any number you can create) + 1

___________________
Emps

FAQs: Emperor

69

:::11oh1:::

I'm inclinded to think that n+1 is an expression and not a number.

I don't get it. I'm eager to hear the answer.

. . : slicePuzzle

All valliant attempts, but whatever number you guys create times zero is zero.

---
"The Mystery of Life"
Vol. 841, Ch. 26
"All life begins with Nu and ends with Nu. This is the truth! This is my beleif! ...at least for now." - Chrono Trigger
><>

Ohhhhh I see its a riddle - its been a while since we did this.

Then my guess is that it is the great Leveller of all numbers the Omega to their Alpha: 0

___________________
Emps

FAQs: Emperor

No... How could zero be the greatest number? It has no value whatsoever. And zero times zero equals zero too.

---
"The Mystery of Life"
Vol. 841, Ch. 26
"All life begins with Nu and ends with Nu. This is the truth! This is my beleif! ...at least for now." - Chrono Trigger
><>



[This message has been edited by Ruku (edited 09-12-2003).]

Ruku: Just to be sure we are all on the same page - this is a riddle and you know the answer and you want us to come up with the answer.

With that as my starting point I'll go with:

Is it i - the square root of -1?

I'm guessing it is great as in 'Alexander The' and not > but.........

___________________
Emps

FAQs: Emperor

0i is still zero though, Emps.

Along similar lines to Emps, my vote goes to pi.

[Edit: Which I realize is still 0 when multiplied by 0.

[This message has been edited by Lord_Fukutoku (edited 09-12-2003).]

I'd think about it a bit longer, but I'm still trying to figure out how to change an NFA with two states & two epsilon transitions into a DFA. It's proving to be um... difficult ><

Intution says it's some sort of undefined number. Like x/0 (which when multiplied by 0, doesn't exist).

[This message has been edited by Raptor (edited 09-12-2003).]

n/0? Isn't that infinite?

Eh, n/0 is "undefined." The limit of n/x as x goes to zero from the positive side is infinity, though.

The answer can't be any finite complex number, since all such numbers times zero equals zero. According to Ruku, it's not infinity either, nor is it eleventy-twelve.

Well, I'm stuck.

Is it NaN? =)

Ah yes, you guys are getting closer... I said it had to be a complex number and Emps and the rest of you guys are on the right track... No its not the sq.rt. of -1. NaN?

And yes I guess you could call this a riddle... I was trying to come up with some rhyme but I stink at poetry.

---
"The Mystery of Life"
Vol. 841, Ch. 26
"All life begins with Nu and ends with Nu. This is the truth! This is my beleif! ...at least for now." - Chrono Trigger
><>





[This message has been edited by Ruku (edited 09-13-2003).]

quote:

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Is it i - the square root of -1?

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Emperor, you can't write the square root of a negative number. i is defined by i²=-1

Otherwise, anybody could write very funny things.



Therefore : -1 = 1 hehehe

Also, the mathematic student in me screams when he sees expressions divided by 0, it is forbidden to write such expressions


As to the answer, it is probably 'just a joke' with a number, because I don't know any complex number that would not be equal to 0 if multiplied by 0. Some expressions could fullfil this requirement, but we wouldn't be talking of numbers but rather of mathematical expressions or limits.



Edit : using an image rather than ambiguous notations.

[This message has been edited by Moon Shadow (edited 09-13-2003).]

Quite a beautiful post Moonshaddow... I don't really know how you came to 1=(-1)... Anycase you didn't find the answer... The other guys were on the right track though.

---
"The Mystery of Life"
Vol. 841, Ch. 26
"All life begins with Nu and ends with Nu. This is the truth! This is my beleif! ...at least for now." - Chrono Trigger
><>

8

Nope....... 8*0=0. Nullified. Should I give off a hint?

---
"The Mystery of Life"
Vol. 841, Ch. 26
"All life begins with Nu and ends with Nu. This is the truth! This is my beleif! ...at least for now." - Chrono Trigger
><>

Actually, I think krets had something there ...

Ruku, NaN is a JavaScript value which stands for "Not a Number." You get it by multiplying a number by a string or something.

Moon Shadow: I don't understand how you started off your little equation - how is -1 equal to the cube root of itself?

Slime :

Any root of 1 is equal to 1. Here I played with a negative number under the root (which is usually forbidden) and the power of the root to achieve a negative number.

You have to agree that :

(-1)^3 = (-1) * (-1) * (-1) = -1

Therefore if you apply a cubic root to both the left and right parts of this equation, you'll find that the cubic root of (-1)^3 (= -1) is equal to the cubic root of (-1). Try with a calculator, you'll see.

More generally, any number written a^(x/y) can be written also like the y-th root of a^x.

The former equation I posted is rigorous, except that it is forbidden in mathematics to write negative numbers under a root, because it can lead to such results.

Ruku :

A little hint would be welcome indeed.

[This message has been edited by Moon Shadow (edited 09-14-2003).]

quote:

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Also, the mathematic student in me screams when he sees expressions divided by 0, it is forbidden to write such expressions.

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Actually, that's not true. It's a common myth that you "can't divide by zero." In reality, you can divide by zero all you want - you simply get the value "undefined" by doing so. 3/0 = undefined.

A number of theorems also include the condition that they only work when something is "a non-zero real number."

However, neither of these facts mean that you *can't* divide by zero.

Similarly, you can take the square root of a negative number all you like, and you get the undefined value by doing so. [edit: correction, you get a complex/imaginary number by doing so.]

That said, I'm trying to figure out what's wrong with the equation you posted. I don't believe the problem is taking the cubic root of -1, I believe that may be legal. I suspect the problem actually lies in the conversion from (-1)^(6/2) to cuberoot((-1)^2), which may not be a legal conversion for negative numbers. I don't know, I'll have to do some research on it or something.

[This message has been edited by Slime (edited 09-14-2003).]

Both Raptor and Slime are very close to the answer... BIG HINT. But be prepared to defend your answer.

---
"The Mystery of Life"
Vol. 841, Ch. 26
"All life begins with Nu and ends with Nu. This is the truth! This is my beleif! ...at least for now." - Chrono Trigger
><>

my guess: the largest number in the universe is unknown.



[edit - typo]

[This message has been edited by velvetrose (edited 09-15-2003).]

Ah well this is a very controvercial number. And yes, whoever said that, it is NaN (Not a Number). Or at least a "real" number. Sorry 'bout being so late on this one.

---
"The Mystery of Life"
Vol. 841, Ch. 26
"All life begins with Nu and ends with Nu. This is the truth! This is my beleif! ...at least for now." - Chrono Trigger
><>

http://www.cs.utah.edu/flux/fluke/html/sa-flukeref/node20.html

Yep, Slime's right.
The correct conversion is: (-1)^(2/6) = (sixth-root(-1))^2 ... Not (-1)^(2/6) = (sixth-root(-1^2))

..any number you care to state + 2

Is it indeterminate?

Lord_Fukutoku: I'm not actually sure if there's a problem with the conversion from (-1)^(2/6) to 6th-root((-1)^2). I think the problem is more subtle. I'm wondering if it has to do with the subtle difference between "square root" and the radical sign.

how 'bout x+1, with x being the currently known (or theorized) highest number.

Xpirex and Counterfeit Bacon, both your numbers multiplied by zero are zero. Not the greatest number. Slime, if you ment, "indefinate", yes it is.

---
"The Mystery of Life"
Vol. 841, Ch. 26
"All life begins with Nu and ends with Nu. This is the truth! This is my beleif! ...at least for now." - Chrono Trigger
><>

what does multiplying a number by 0 have to do with it being the greatest number?
I thought all numbers when multiplied by 0 are 0, even fractions or anything.

[This message has been edited by Gilbert Nolander (edited 09-16-2003).]

Not necessarily. As has been pointed out, there are expressions that when multiplied by zero, don't necessarily equal zero.

(n/2) * 2 = n

(n/0) * 0 = NaN (and definitely != n)

you can't divide a number by 0

ah.nevermind....

The answer is 2.54

Raptor! You're right there!

And yes you can divide a number by zero. But you'll get an error on a calculator. Its called an "imaginary number".

---
"The Mystery of Life"
Vol. 841, Ch. 26
"All life begins with Nu and ends with Nu. This is the truth! This is my beleif! ...at least for now." - Chrono Trigger
><>

so are you saying that an imaginary number is the greatest number?

quote:

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and yes you can divide a number by zero. But you'll get an error on a calculator. Its called an "imaginary number".

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You do not get an imaginary number by dividing by zero. If you divide by zero on a calculator or computer you'll get a NaN as answer, which was stated above by Slime... The fraction a/b will go towards infinity as b approaches 0. This has nothing to do with imaginary numbers.

Imaginary numbers are those that are written a+ib, where the i is the same i that is beeing discussed above.

This thing with -1=1 is interresting. A professor showed us the 'proof' last semester and explained what is wrong with it, now I just have to figure out where my notes from that lection is...

btw, the greatest number is the Divine Proportion

_________________________
"There are 10 kinds of people; those who know binary, those who don't and those who start counting at zero"
- the Golden Ratio -

[This message has been edited by Veneficuz (edited 09-16-2003).]

so ruku, what is the greatest number now? the imaginary one?

You did not ask what the effect of multiplying a number by zero would be.. you asked what the biggest number was... this is a whole different thing, no hidden variables please.

That's like asking what is the biggest mountain in the world is? ...and I say Everest... and you say Everest times zero = nothing and so you conclude Everest does not exist anymore... mmm I don't have time for this foolery.



[This message has been edited by Xpirex (edited 09-16-2003).]

Well then just to keep everyone going, you are right about x/0 not being a real number. It's called an Imaginary Number. http://www.math.toronto.edu/mathnet/answers/imaginary.html

The answer is... 1/0, because 1/0*0=1 You can do this with any number really... 939248323.25248/0*0=939248323.25248. So therefore, this set of imaginary numbers are the largest number in the world . And sorry, I didn't pick up the x/0 part until I just thought now, Geez you can substitute any number for one and it'll come out the greatest... Crud!

---
"The Mystery of Life"
Vol. 841, Ch. 26
"All life begins with Nu and ends with Nu. This is the truth! This is my beleif! ...at least for now." - Chrono Trigger
><>

ok, once again:

~starts SCREAMING~
x/0 IS NOT AN IMAGINARY NUMBER !!!
IT AINT GOT NOTHING TO DO WITH IMAGINARY NUMBERS AT ALL !!!
IT AINT GOT NOTHING TO DO WITH IMAGINARY NUMBERS AT ALL !!!
IT AINT GOT NOTHING TO DO WITH IMAGINARY NUMBERS AT ALL !!!
IT AINT GOT NOTHING TO DO WITH IMAGINARY NUMBERS AT ALL !!!
IT AINT GOT NOTHING TO DO WITH IMAGINARY NUMBERS AT ALL !!!
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAARGH!!!
~runs off screaming and repeatedly banging his head on walls~

so.....every number that exists is the single "greatest" number aobve all.....

because if you do things to it that you can't *really* do you can make it the same as it was before you didn't do anything to it.....?

how cool.....





[This message has been edited by DL-44 (edited 09-17-2003).]

i is an imaginary number, like Emps guessed way early on, and other people mentioned earlier. i = square root of -1 or somesuch.

x/0 isn't any imaginary number, that's a good ol "undefined". (Some argue it's infinity, some undefined, same thing in my book... Though I do recall someone in our school got sent to ISP (in school suspension) for arguing with the math teacher that #/0 = infinity.. heh.)

imho, there is no "greatest number" besides the whole infinity+1 thing. (Actually, I prefer infinity^infinity. (infinity to an infinite power.)

-Xel


[This message has been edited by Xel (edited 09-17-2003).]

quote:

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Some argue it's infinity, some undefined

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I don't see how that's even arguable...

For any x, and given the equation x/n, you get two different possibilities for its limit as n approaches zero (as Slime has already pointed out for us). You get -infinity from as n approaches zero from the negative side, and +infinity as n approaches zero from the positive side. And simply put, +infinity != -infinity. I'd certainly call that "undefined."

*shrugs* I guess to me, arguing that n/0 is infinity is kind of like trying to say .9999999999999999999 (etc) isn't 1.



[This message has been edited by Raptor (edited 09-17-2003).]

quote:

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arguing that n/0 is infinity is kind of like trying to say .9999999999999999999 (etc) isn't 1.

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I've actually seen some very long arguements between math geeks, and people who refuse to believe that 0.999(rep) = 1.

Yet those same geeks would subscribe to the methods of rounding which would turn that 0.9(rep) into 1

Well 0.9999(rep) isn't 1 - you could get infinately close to it but you'd never reach it. On the other hand if you were covering a room with carpeting, I wouldn't say that I needed 0.999999(rep) yards, I'd say I just needed 1.

Hey its a controversial matter. Can you do anything in the real world with 1/0? Nope. Can you do it with math? Yep. Now you can go mouthing off to teachers saying that not everything multiplied by zero equals zero.

---
"The Mystery of Life"
Vol. 841, Ch. 26
"All life begins with Nu and ends with Nu. This is the truth! This is my beleif! ...at least for now." - Chrono Trigger
><>

Dan: people who don't believe are either
a) too blind to the truth to know when something is obviously spelled out for them or,
b) see a).

quote:

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Well 0.9999(rep) isn't 1 - you could get infinately close to it but you'd never reach it.

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Here we go...

eq1) .99999(rep) = 9/10 + 9/100 + 9/1000 + 9/10000 + ... + 9/10^n + 9/10^(n+1) + ... =

eq2) 9/10(1 + 1/10 + 1/10² + 1/10³ + ... + 1/10^n + 1/10^(n+1) + ... ) =

By definition of a geometric series; the sum of a*r^(n-1) from n = 1 to infinity =

eq3) a*r^0 + a*r + a*r² + a*r³ + ... + a*r^n + a*r^(n+1) + ...

Which, if it's convergent (it approaches a finite value - in this case, 1) =

eq4) a/(1-r) (edit: note that eq4 is only valid if r < 1)

Note that eq2 and eq3 are simliar. Note also that eq3 = eq4. Substituting eq2 into eq3 and converting it into eq4 we get the following:

(9/10)/(1-1/10) = .9/.9 = 1

Substitution yields eq1 = eq2 = 1; which also gives .9999(rep) = 1.



Now ask yourself the question: what's the smallest number greater than zero?



[This message has been edited by Raptor (edited 09-17-2003).]

Actually, I do remember a little trick one of our math teachers pulled on us kids back in 7th or 8th grade.. I'm absolutely positive there was something "wrong" with the way he did it, but we for the life of us couldn't figure out what it was.. but according to his equation wrangling trick, .9 equalled 1. Was funny. (Now I'll hafta go find this teacher again and see if he still remembers it.)

quote:

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Yet those same geeks would subscribe to the methods of rounding which would turn that 0.9(rep) into 1

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No rounding necessary, they're exactally the same number. (Any 2 real numbers which are different will always have an infinate number of real numbers between them)

1/9 = 0.111(rep) 2/9 = 0.222(rep) {3; 4; 5; 6; 7; 8; } /9, all the same. 45/99 3667/9999 - test em all out... observe the pattern. Now try 9/9.

...or you can prove it with algebra.


x = 0.99999999......

10x = 9.99999999......


9x = 10x - x = 9.999999.... - 0.9999999.....

9x = 9

x = 1



(i find it a little easier than induction)

reitsma

Bleh. My brain won't function this early. I'll just pretend I understand what you're talking about.

---
"The Mystery of Life"
Vol. 841, Ch. 26
"All life begins with Nu and ends with Nu. This is the truth! This is my beleif! ...at least for now." - Chrono Trigger
><>

Slime - Re: "I'm not actually sure if there's a problem with the conversion from (-1)^(2/6) to 6th-root((-1)^2). I think the problem is more subtle. I'm wondering if it has to do with the subtle difference between "square root" and the radical sign."

Yea, that was just what I pulled off the top of my head from the last time I had to convert between exponents and radicals (which has been awhile). But after searching a bit, it seems the two are equivalent (at least as long as you're working with the positive numbers): http://www.tpub.com/math1/8c.htm

I'll see if I can't spend a bit of time playing with that eq to find something maybe... ::shrugs::

l've looked some more at it and the problems with the proof is that the exponents rules aren't 'properly' defined for negative numbers. So error is spread among the following parts: (-1)^1/3 = (-1)^2/3=6th root((-1)^2), the 'biggest' error being in the first equal-sign. Talked to one of the math professor here at the Uni as well, and he said the same

_________________________
"There are 10 kinds of people; those who know binary, those who don't and those who start counting at zero"
- the Golden Ratio -

I think there are several differences in the way we are taught mathematics in France and in the USA.

- About dividing by 0 : your calculators will always return 'undef' because this expression doesn't exist. You can divide by expressions that tend towards 0 (when speaking about limits), but dividing by 0 is a mathematical nonsense. You can divide by 0, but it doesn't mean anything. Well, at least in France. And as MW finely said it, it is not an imaginary number. It simply doesn't exist.

- About the expression I formerly wrote : I asked a math teacher about it. What is wrong in this expression is writing roots of negative numbers. In fact, it is possible to write the roots of negative numbers, but we shouldn't, we should use complex numbers instead. For example, writing 'sqrt(-1)' is possible (although mathematically incorrect, as dividing by 0 is incorrect), but we should instead write 'i'.

But frankly, there are several differences about how everyone is taught this, and I won't rip my hair with you about that



[This message has been edited by Moon Shadow (edited 09-20-2003).]

quote:

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- About dividing by 0 : your calculators will always return 'undef' because this expression doesn't exist. You can divide by expressions that tend towards 0 (when speaking about limits), but dividing by 0 is a mathematical nonsense. You can divide by 0, but it doesn't mean anything. Well, at least in France. And as MW finely said it, it is not an imaginary number. It simply doesn't exist.

---

No difference here in the US. It's mathematically undefined; some people are just mis-informed.

quote:

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- About the expression I formerly wrote : I asked a math teacher about it. What is wrong in this expression is writing roots of negative numbers. In fact, it is possible to write the roots of negative numbers, but we shouldn't, we should use complex numbers instead. For example, writing 'sqrt(-1)' is possible (although mathematically incorrect, as dividing by 0 is incorrect), but we should instead write 'i'.

---

From what I've learnt about this one should optimally not write the root of negative numbers, but a proof can be valid even if it contains the root of a negative number. One just have to remeber to define what one means by that, since the normal root isn't defined for negative numbers. In this case we could have defined sqrt(-1) as isqrt(1) and that problem would have been 'solved'. This is legal as long as the new mathematical rules applying to normal roots still are valid in with the new definition.

This page from the Toronto Uni explains the same thing, but in a different way...

_________________________
"There are 10 kinds of people; those who know binary, those who don't and those who start counting at zero"
- the Golden Ratio -

Anyone with a computer knows that the greatest numbers is a 1 and a 0.


The programmer's national anthem is 'AAAAAAAAHHHHHHHH''

Wolfen's Sig Site

quote:

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x = 0.99999999......
10x = 9.99999999......
9x = 10x - x = 9.999999.... - 0.9999999.....
9x = 9
x = 1

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ACK! You guys are shattering my world view!

I'd like to see the proof that shows 10 x 0.999(rep) = 9.9999(rep)
If there's an infinate number of decimal places, can you really move the decimal over by one? I don't think so. (I'm sure in most cases it will work, but assuming it works in every case isn't very mathematical, and since 0.999(rep) can't be expressed as a fraction (that is, until after you prove that it equals 1), I don't think it's fair to say that you can determine the outcome of it being multiplied be any real number)

Raptor and Veneficuz : thanks to both of you for the little notifications. My vision of mathematics was being questioned, I feel better now

I'll leave again for a whole week soon, but it seems to me that this topic interested a lot of people. Therefore, I think that if there are some folks around who know other math riddles, I encourage them to post them.

Hey, who said once on this forum that our ability to program wasn't limited by our intelligence, but rather by our level at mathematics ?

[This message has been edited by Moon Shadow (edited 09-21-2003).]

quote:

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I'd like to see the proof that shows 10 x 0.999(rep) = 9.9999(rep)
If there's an infinate number of decimal places, can you really move the decimal over by one?

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Yes, IMO.
Because it´s obvious that 0.9 x 10 = 9 and 0.99 x 10 = 9.9 and from there you just keep going - it would be unlogical if there was a point where this suddenly wouldn´t be correct anymore.

This should be true for an infinite number of decimals, too, because Infinity = (Infinity + 1) .

Actually, if you want to get technical... 10 * .999(rep) = 1.

Since .999(rep) = 1 and all.

quote:

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Actually, if you want to get technical... 10 * .999(rep) = 1.
Since .999(rep) = 1 and all.

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I think you're mistaken. if .999(rep) = 1 then 10 * .999(rep) = 10 * 1 whcih equals 10 not 1

My poor head hurts...

dan - this is the technique for converting recurring decimals to fractions:

x = 0.34343434.....

100x = 34.343434.....
99x = 34

x = 34/99


see?


...and as i recall, this technique has also been supported bu induction, etc... plus it's fun.

reitsma

Oy this topic is huge. Anywho, yes that is a fun trick. ^^ So you can argue that any number over zero is the greatest number, and that 1=.999(rep) and that white is black and up is down... but I'd like to see the white/black up/down arguments... That'd be interesting.

---
"The Mystery of Life"
Vol. 841, Ch. 26
"All life begins with Nu and ends with Nu. This is the truth! This is my beleif! ...at least for now." - Chrono Trigger
><>

Now, what does any of this have to do with my future career as a professional basketball player?

(monday morning)

quote:

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I think you're mistaken. if .999(rep) = 1 then 10 * .999(rep) = 10 * 1 whcih equals 10 not 1

---

...

note to self: don't post when drunk.

[This message has been edited by Raptor (edited 09-22-2003).]

quote:

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Now, what does any of this have to do with my future career as a professional basketball player?

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Just think how confused all the other players will be when you ask them these questions or start rambling about the proofs. And as they stand there dumb-struck you can easily walk over the field and score

_________________________
"There are 10 kinds of people; those who know binary, those who don't and those who start counting at zero"
- the Golden Ratio -

but isn't

quote:

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939248323.25248/0*0=939248323.25248

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is still equal to 0?

quote:

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but isn't
------
939248323.25248/0*0=939248323.25248
------
is still equal to 0?

---

Divding by zero is an illegal operation, so I think we all agreed that Ruku's 'answer' was wrong. There is no greatest number according to his definition, that definition being that the number multiplied by zero should not equal zero.


_________________________
"There are 10 kinds of people; those who know binary, those who don't and those who start counting at zero"
- the Golden Ratio -

[This message has been edited by Veneficuz (edited 09-24-2003).]

quote:

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x = 0.99999999......

10x = 9.99999999......


9x = 10x - x = 9.999999.... - 0.9999999.....

9x = 9

x = 1

---

Except that subtraction and addition supercede division and multiplication in the precedence of function. Your expression should read

9X = (10-1)X not 9X = 10X - X

Regardless of that. X is defined. Why redefine it? .9999.... != 1 it will always be .000000....1 short of 1. To believe otherwise is to believe that infinity doesn't exist.

*points up at using a geometric series to define .999(rep) = 1*

That proof is sound. .999(rep) = 1, and while I'm at it, .0000(rep)...1 doesn't exist, either. Same reason as .999(rep) doesn't exist. You can't have a "smallest positive real number," or a "greatest positive real number less than one."

More simply, how could you have a decimal, followed by an infinite number of zeros, ending with a one?

quote:

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9X = (10-1)X not 9X = 10X - X

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Both of the above statements are legal, and they mean exactly the same...

I had some trouble accepting that 0.999(rep)=1 in the beginning, but both of the proofs offered for are valid as far as I can see and locigaly it is almost ok as well. The difference between .9999(rep) and 1 will approach 0 as the number of decimals goes towards infinity. So after an infinity number of decimals the difference should be 0, eg 0.999(rep)=1. Only problem now is seeing how this fits in fit the 'algebra's fundamental law' (or something like that) which states that in between any given two numbers there is an infinite of other numbers. So even if the difference between .999(rep) and 1 goes towards 0 after an infinite number of decimals there will always be an infinite other numbers between 0.999(rep) and 1 as long as the difference is greater than 0...

_________________________
"There are 10 kinds of people; those who know binary, those who don't and those who start counting at zero"
- the Golden Ratio -

So then, by this reasoning anything that ends in .99999(rep) actually doesn't?

5.9999.... is really 6.

0.599999.... is really 0.6?

And, just going from what you said, Raptor... 0.9999(rep) doesn't exist... therefore it equals 1?

quote:

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More simply, how could you have a decimal, followed by an infinite number of zeros, ending with a one?

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Well. Why couldn't you? 1 - 0.99 = 0.01 does it not? Why shouldn't 1 - 0.999(rep) = 0.000(rep)1 Where the places after the decimal are equal? Since we're ceasing infinity to perform any sort of calculation at all you'll always get the afore-mentioned result. If .999(rep) is infinitely approaching 1 - Who decided that infinty ended and there was zero difference? Measurable or not, infinity determines that 0.9999(rep) != 1, by my understanding of its definition. As I said. Either it doesn't work, or it does and you don't believe in infinity. I'm trying to understand the meat behind why you believe that .9999(rep) = 1

Also... why does 10X - X != X +X +X +X +X +X +X +X +X?

I'm truly curious, I'm not trying to be difficult. I'm just looking for more... depth of reason to believe that .999(rep) = 1 until I'm out of reasons that it doesn't... I'll be skeptical. So please don't leave me floundering in the mathmatical quagmire.

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So then, by this reasoning anything that ends in .99999(rep) actually doesn't?

5.9999.... is really 6.

0.599999.... is really 0.6?

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Yes, Yes and Yes.

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Why shouldn't 1 - 0.999(rep) = 0.000(rep)1 Where the places after the decimal are equal?
Since we're ceasing infinity to perform any sort of calculation at all you'll always get the afore-mentioned result. If .999(rep) is infinitely approaching 1 - Who decided that infinty ended and there was zero difference?

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Damn, you got it backwards again. There IS zero difference BECAUSE infinity does NOT end. If 1 - 0.999 (rep) did not equal zero, YOU´d have to tell ME at which decimal place it would start differing from zero. And whatever your answer, it would be wrong, because we agreed above that there is an INFINITE number of zeroes before the one. And because infinity does NOT end, there is NO "one".

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Also... why does 10X - X != X +X +X +X +X +X +X +X +X?

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The point was that 10x -x indeed equals x+x+x+x+x+x+x+x+x and 0,999(rep) equals 1 for this very reason.

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I'm truly curious, I'm not trying to be difficult. I'm just looking for more... depth of reason to believe that .999(rep) = 1 until I'm out of reasons that it doesn't...

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You are. You just don´t notice.

Let me close with a quote that seems very appropriate here:

"In mathematics you don't understand things. You just get used to them."
-Johann von Neumann (1903 - 1957)

Hmmmm... I think I can accept that... That is a far better explaination then what I was able to find online.

I think I need to thump a few of my math teachers skulls.

Man, Pre-trig's hard enough without trying to convince people that 1=0.999(rep) but some how my science teacher convinced me that 100+10=100... Don't ask me how or why.

---
"The Mystery of Life"
Vol. 841, Ch. 26
"All life begins with Nu and ends with Nu. This is the truth! This is my beleif! ...at least for now." - Chrono Trigger
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some how my science teacher convinced me that 100+10=100... Don't ask me how or why.

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I promise we won´t ask, if you promise you´ll NEVER NEVER NEVER tell us, asked or not. Because I´m quite sure the explanation would make me bang my head against some more walls and I still got a headache from last time...

Well it had to do something like this... Sorry, just had to explain so you guys wouldn't think I'm a weirdo.

+100
10
____
110

Right? No! How do we know what the hundredths digit on the ten number is? it may really be x10. So there fore we have to round to the nearest place value. 110 rounded equals 100. [Lets hope this formatting works ]

[Edit: looks like it didn't. Can't you under line using the <u> tag ('cept with brackets, not Greaterthen signs)]
---
"The Mystery of Life"
Vol. 841, Ch. 26
"All life begins with Nu and ends with Nu. This is the truth! This is my beleif! ...at least for now." - Chrono Trigger
><>



[This message has been edited by Ruku (edited 09-27-2003).]

I believe it's called accuracy. If I remember correctly, a line was put over a zero if it was accurate. Otherwise, a number was accurate only for the non-zero digits.

In the above example of 100 + 10, it would equal 110 if the tens is accurate in 100. But there is no line over the tens (I'm assuming the science teacher didn't have a line over his 100), so 100 is correct.

The general rule is to use the least amount of accuracy...?

Gremlin corection:

100 + 10 = 110
if the tens in 100 is accurate and the ones in 10 is accurate.

Googleplex^Googleplex

Now that is a big number!

Accuracy or not, it would be IDIOTIC to make your inaccuracy even bigger by ignoring the fact that you KNOW your result will be bigger (by 10, 11, or even 19) than the 100 (or 110, or 190) you started with.
In science what you do is find out (or estimate) how big your inaccuracy is and write it like this:

(150 +- 50) + (15 +- 5) = ( 165 +- sqrt(50^2 + 5^2) ) = ( 165 +- 50,25 )

And just so you don´t think now you understood it, here´s the whole story:
http://mathworld.wolfram.com/ErrorPropagation.html

BTW, as a tip for all of you, this site has everything you never wanted to know about maths and then some:
http://mathworld.wolfram.com/



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We hang the petty thieves and appoint the great ones to public office.
Aesop (620 BC - 560 BC)

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In science what you do is find out (or estimate) how big your inaccuracy is and write it like this:

(150 +- 50) + (15 +- 5) = ( 165 +- sqrt(50^2 + 5^2) ) = ( 165 +- 50,25 )

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But there are also a lot of places in science where you only give the answer in 'size', for example <some fancy equation> almost equal 10^16. It doesn't matter if it is 4.5*10^16 or 3.4*10^16. The answer is still right enough as long as the exponent is right.

There are also examples where you can say 'the number n in this equation is BIG, so we approximate to infinity'. It isn't unknown either to say 'this number is so small compared to this one, so might as well remove the small number at once and be done with it'.

And to keep the whole thing going there are many places in science where they 'overlook' answers to equations since they don't fit the theory, or that they allready found an answer that works.

So the accuracy in numbers used in science can vary a lot, but somehow they make it all work anyway

_________________________
"There are 10 kinds of people; those who know binary, those who don't and those who start counting at zero"
- the Golden Ratio -

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But there are also a lot of places in science where you only give the answer in 'size', for example <some fancy equation> almost equal 10^16. It doesn't matter if it is 4.5*10^16 or 3.4*10^16. The answer is still right enough as long as the exponent is right.

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This is only done for when you just need a very rough estimate, or when your data is too unprecise to make a better statement. If you are going to do further calculations with your result, you better make it as precise as you can, and, even more important, give a good estimate of the error, because that allows you to judge the significance of your result.

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There are also examples where you can say 'the number n in this equation is BIG, so we approximate to infinity'. It isn't unknown either to say 'this number is so small compared to this one, so might as well remove the small number at once and be done with it'.

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That´s right. It´s done all the time, and that´s one of the cases where you only calculate the exponents, to see which numbers are so small you can kick them out of the calculation. In my above example the uncertainity of the 15 would have been ignored, for example, as it only contributes 1% to the error. But you usually wouldn´t ignore adding 10% to the result itself, by totally ignoring the 15.

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And to keep the whole thing going there are many places in science where they 'overlook' answers to equations since they don't fit the theory, or that they allready found an answer that works.

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I´m shure this happens all the time, too, although it shouldn´t. Or maybe it should, because when your result is significantly different from what you expect, the probability that you made a mistake is a lot higher than having discovered a new law of nature.

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We hang the petty thieves and appoint the great ones to public office.
Aesop (620 BC - 560 BC)

[This message has been edited by MW (edited 09-29-2003).]

Oh, BTW,

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to keep the whole thing going

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NOOOOOOOOOOOOO!!!!!!

Well I'm sure you all are glad that you have reached ultimate peace and obtained a higher level... this is about to reach 100 posts... As am I... Gotta do a sig for that >.> Big number for me ^^

---
"The Mystery of Life"
Vol. 841, Ch. 26
"All life begins with Nu and ends with Nu. This is the truth! This is my beleif! ...at least for now." - Chrono Trigger
><>