To begin this thread, I'd like to post a gigantic warning:

I DON'T KNOW A GODAMN THING ABOUT MATH. I'VE FAILED HIGHSCHOOL MATH TWICE.

Now that that's done, let's continue:

.99 Repeating != 1


right?

Wrong. 1/3rd of .99 repeating is .33 repeating... which is also 1/3rd of 1. thus 1== .99 repeating.

Is this a fault of computers being unable to calculate an infinate number? Does it make math itself incorrect? Does that mean that infinite is just a side effect of our flawed math system?

JediKirby

the more nines you have, the closer the difference between that and 1 to zero

the number of nines is approching infinity, the difference is approching zero

You mean .99 repeating divided by .33 repeating.

But anyway, I don't know anything about infinite mathematics. TRUE infinite mathematics ( = no rounding allowed)

And now a paragraph based on an excerpt from The Hitchhiker's Guide to the Galaxy:

(Universe statistics)

Inhabited Planets: 0
While there are indeed many inhabited planets in the known universe, there are an infinite number of planets in the universe because the universe is infinitely large. But since not all of those planets are inhabited (which we know), the number of inhabited planets is zero, because any number divided by infinity is as close to zero as can be.

That explains why you think einstein's theories are flawed... all of your scientific knowledge comes from the pseudo science of Hitchiker's Guide to the Galaxy.

Well, not all of it. :em321:



BAAA futurepost! *hits Zecks* You're it!

HBey, you're attacking the wrong guy. Matterialize ceded the argument. Its that capt fellow that is refusing to see reality

[Edit]Wow, double futurepost

Thank you.

Actually, the problem is simple, 1/3 != .333333 repeating.

This is a failing of the decimal number system in which there is not a proper representation for this value. Instead we simply assume .33333 repeating to be an approximation for the value of 1/3. Given, the more digits you add, the better approximation of 1/3 you get, but it will never actually equal 1/3.

All number systems have similar limitations, the binary system can only accurately represent fractions of a power of 2 (IE 1/2, 1/4, 1/8...)

If I recall, this all traces down to prime factors: A number system can only accurately represent fractional values if all the prime factors of the denominator are also prime factors of the base of the number system.

Basically, the Decimal system has the prime factors of (1,2, and 5) so anything with a denominator with a prime factor not in that set cannot be accurately represented in the decimal number system (factors such as 3,7,11,13,17...)




P.S. Sorry Zecks, FUTURE POST!!!!

I believe it's time to start the lesson on LIMITS.... Mwuahahahaha...

Calculus strikes again!

Ahhh, but remember, just because the Limit of F(x) as x approaches a is b does NOT MEAN that F(a) = b ...

Yes, that is a problem with the calculator. They do not keep going to infinity.

Did Zecks just get future posted by just about everyone?

The limit as you add more 9's approaches 1, but doesn't get there.

But if you write 0.99 with a dot over each of the 9s to represent them going to infinity, then they DO equal 1 (strangely).

I had a drunken debate with a mathematician about this, and this was (if i remember rightly) the conclusion we came to.

The limit as you add more 9's is1.

sum((0.9 / 10^n) ...), the limit of the sum as n approaches infinity is 1.

or the sum of the infinite geometric series:

S = a / (1 - r); a = 0.9, r = .1
S = 0.9 / (1 - 0.1) = 0.9 / 0.9 = 1.

S = 1.

So Martyn + Beer + Maths girl with lovely jumblies == right!

This is a constantly debated subject, and as far as I know, neither side has been proven wrong.

Nope, if it's REPEATING/RECURRING it goes to infinity, becomes the sum of an infinte series and becomes 1.

Just like that.

S = 0.3 / (1 - 0.1) = 0.3 / 0.9 = 1 / 3 = 0.33333....
S = 0.6 / (1 - 0.1) = 0.6 / 0.9 = 2 / 3 = 0.66666....
S = 0.9 / (1 - 0.1) = 0.9 / 0.9 = 1 / 1 = 1

Anybody who is still having trouble understanding this concept should research 'real numbers', which where only properly understood by mathematicians fairly recently.

Essentially any number that has a repeating zero may also be expressed as a different number with a repeating 9. It's due to the properties of infinity, which is a fairly difficult concept for most people to grasp. (Something I'm happy to say I don't have a problem with). This isn't a subject up for debate.

Look at it from the other direction. Instead of saying '0.99999... approaches 1 but never reaches it', think about how large a number you'd need to subtract from 1 to get 0.9999...! No matter what number you get, it's always going to be too large. The smallest possible number you can subtract from 1 is zero, which means you still end up with:

1 - 0 = 0.9999.
1 = 0.9999.

Jon'C, dont go confusing people with interesting, but unrelated mathematical concepts... it might hurt their heads... at least until I have had my chance

Anyway, how about this, lets try a base 3 number system (0,1,2).

Decimal=Trinary
0=0
1=1
2=2
3=10
4=11
5=12
6=20
7=21
8=22
9=100
10=101
...=...

Thus
1/3 = .1
2/3 = .2
1/9 = .01
2/9 = .02
3/9 = 1/3 = .1
4/9 = .11
5/9 = .12
6/9 = 2/3 = .2
7/9 = .21
8/9 = .22
9/9 = 1

Therefore

1/3 + 1/3 + 1/3 = 1
and
.1 + .1 + .1 = 1

But lets say you want to represent 1/2, 1/5, or 1/7 in trinary? There is no easy way, so you end up with an approximation. Unfortunately I am not yet good enough to calculate these quickly.

Well, from Douglas Adams to Scott Adams,
"'Scientists often invent words to fill holes in their understanding. These words are meant as conveniences until real understanding can be found. Sometimes understanding comes and the temporary words can be replaced with words that have more meaning. More often, however, The patch words will take on a life of their own and no one will remember they were only intended as placeholders.
'For example, some scientists describe gravity as ten dimensions all curled up. But these aren't real words- just placeholders, used to refer to parts of abstract equations. Even if the equations someday prove useful, it would say nothing of the existence of other dimensions. Words such as dimension and field and infinity are nothing more than conveniences for mathematicians and scientists. They are not descriptions of reality, yet we accept them as such because everyone is sure someone else knows what the words mean.'
I listened. Rocking, mildly stunned.
'Have you heard of string theory?' he asked."
-Scott Adams, God's Debris

-You guys should read it.

For two numbers to be distinct there needs to be a number in between them.
There is no number in between 0.9 repeated and 1, therefore 0.9 repeated = 1.

That's how I see it at least.

Sorry, you're right.

What do you mean by "only recently understood"?

Yeah, there are all sorts of strange things when it comes to infinity. Like, the size of any two non-empty sets of real numbers is the same, but the size of the set of real numbers is larger than the size of the set of positive integers.

And by the way, that's bad form in that last equation. You're assuming that they're equal to begin with!

Did you even read what I wrote?

You quoted my post entirely out of context. That's the dumbest thing I've ever seen in my entire life.

Why is this even a debate? If you don't think 0.999... = 1, go take (and fail because of it) a math class.

We've had like 923483920 threads on this, all of which ended in an absolute proof being posted involving limits, and everyone shutting up or quoting it saying "Win." and the thread dying.

It all comes back to limits doesn't it. But then, limits don't actually hit the number, they just approach it infinitely. When we solve, we simply treat it as though it did hit. I honestly don't believe that we will have a correct answer for this with sufficient proof to leave no doubt in our minds.

One side will prove it to equal 1/1=1 the other side .3333333333repeating*3=.999999repeating

Both are true, yet seem to contradict eachother. Oh well. Maybe someone will find a magic formula to end our troubles before we start saying: win.

Win.




>_>

Except they aren't both true, only the argument that 0.99999~ = 1 is true. The other one is completely and totally false. Number theory says it, the algebra you learn in Jr. High says it, calculus says it, and most importantly I say it. :p

Just because you don't understand something, doesn't make it untrue.

That's a clever way to put it.

Hey, I said you were wrong, and you told me to shut up saying I was wrong...

WELL I HATE TO SAY IT


NO I DONT

YOU WERE WRONG!!

What I don’t get is why people keep obsessing about infinity with this... It’s really not that hard.

.33333333 repeating is NOT EQUAL to 1/3, it is simply an infinitely good approximation of actual value of 1/3.

Therefore the sum of .33333333 repeating + .33333333 repeating + .33333333 repeating is .99999999 repeating, which is NOT EQUAL to 1, but an infinitely good approximation of 1.

In that same way:

0.142857142857142857142857142857 repeating is an infinitely good approximation of the value of 1/7,

0.090909090909 repeating is an infinitely good approximation of 1/11,

0.076923076923076923076923076923 repeating is an infinitely good approximation of 1/13,

if you start adding these up until they should equal one, you will end up with the same anomaly, but I don’t see people arguing a whole lot about that….

[QUOTE=West Wind].33333333 repeating is NOT EQUAL to 1/3, it is simply an infinitely good approximation of actual value of 1/3.[/QUOTE]

Continually repeating this isn't going to make it true. .333... is rational, so by definition it has an equivalent fractional form.

In fact, the real number system is often defined as equivalence classes of rational Cauchy sequences. This both demonstrates the equivalence of a recurring decimal with its fractional form, and requires that .999... and 1 represent the same number.

[QUOTE=West Wind]
.33333333 repeating is NOT EQUAL to 1/3, it is simply an infinitely good approximation of actual value of 1/3. [/QUOTE]

So what's the difference between an infinitely good approximation and that which it approximates?

So in the end, fractions are better representations of parts than decimals?

you are correct, .333 is rational, and does have an equivalent fractional form: 333/100, as you keep adding 3's the fractional form increases correspondingly (3333/1000, 33333/10000, so on) again, the limit as this series progresses towards infinity is 1/3, but it is never actually 1/3 itself.

The point I keep trying to make is that in Decimal notation, there is NO equivalent form for 1/3. True, all rational numbers in decimal form have an equivalent fractional form, however the inverse is not true.

I am not in dispute with the mathematics that indicates that .99999999 repeating must be virtually identical to 1. Any infinitely good approximation should be virtually identical to the number it approximates, however the fact that it is an approximation is what really makes the difference. To make matters worse, it is virtually impossible to actually use the infinitely good approximation; we just end up using finitely good approximations thinking they are infinitely good thinking they are actual values.

At the root, the question all come down to what Naythn is asking, what is the difference between a value and it’s infinitely good approximation? I know this comes up allot in higher mathematics, and I do not consider myself qualified to answer definitively, but I know I have been yelled at previously for not distinguishing between approximations and actual values.

Ultimately, just use 1/3… its better

Hey West Wind, GO TAKE A CALCULUS CLASS, and STOP POSTING YOUR BULL****.