Poll: Does 0.99 Recurring = 1

[Beansprout]

Originally posted by daz
I was going to post that I didn't think Anthony had had any theorems published...

Hehe, he might've done, you never know.

 

[Bodak]

Originally posted by Reezer

Any comparison you do with infinity causes big problems because is not possible to evaluate properly. Hell, mathematitions can't even decide what happens when you do the basic arithmetic operations with it. 1/0 = inf? you would think so, but apparently not, inf/2 = ?.... inf?

If top mathematical brains the world over can't devide those things i don't think a bunch of geeks on a forum will be able to answer it
.

Lim x->0 [1/x] = inf
Lim x->inf [x/2] = inf

I'm guessing your issue is that inf/2 =! "A half an infinity". Think about what infinity is. If you cut it in half at any point, you still "sort of have" an infinity. Generally, you can't plug inf. in as a number, you have to use limits, or think about what's actually going on.

 

[daz]

Originally posted by TheBeansprout
Hehe, he might've done, you never know.

Well, I would guess he's doing his thesis this year as IIRC he's third year maths...

 

[Reezer]

Originally posted by AlphaNumeric
Where did you hear mathmaticians can't use 0.9r? I'd be interested to know.

I wasn't refering to 0.9r. I was refering to infinity which relates to the recuring part... which I thought I made clear by mentioning it in almost every sentence in my post...

 

[Reezer]

Originally posted by Bodak
Lim x->0 [1/x] = inf
Lim x->inf [x/2] = inf

I'm guessing your issue is that inf/2 =! "A half an infinity". Think about what infinity is. If you cut it in half at any point, you still "sort of have" an infinity. Generally, you can't plug inf. in as a number, you have to use limits, or think about what's actually going on.

Sure, but we are talking in the general 0.9r = 1 sense... which doesn't have any limits, unless someone wan't to go back and redefine the discussion, when i'll change my response.

 

[El Gringo]

If you're going to "take the time" to reply to people's posts make sure you read them properly... Where the hell does Reezer say he's referring to .9r?

I seem to recall that in the first "does 0.9r = 1" thread people were pulling hissy fits because they didn't want to accept that there was any other way it could be viewed other than mathematically... And yet now, it's been accepted that it can also be thought of philosophically. How things change...

 

[Anarchy]

Originally posted by Harley
Look at some of my posts, here and in the original thread. Or, simply consider that it involves a critical look at how we do things, and in particular, what infinity means. I gave one example to Alpha. How do you know when a proof is valid? Search for Fermat's Last Theorem and Wiles (on here) for some points.

If still in doubt, then on a more general level take a look at Principia Mathematica by Betrand Russelll and Alfred Whitehead for the application of philosophy to mathematics.

Hmm, I've read a few of your posts and I'm not sure I get what your saying. This is how I understood it:
Infinity is a mathematical concept, which we rely on being correct to calculate if 0.9r is equal to 1.
We believe in the concept of infinity because we haven't proven that it's wrong (similar to Wiles theorem), but it's possible that there's a case when it doesn't hold.

But surely until this case is found, then it is fine to use the infinity concept as it is (although you'd have to be aware if it is wrong).

Also, you talk about infinity not being quantifiable, but surely you can just use "∞" - in a similar way that we use "∏" to denote pi. I guess you mean quantifying it so its 9999999... etc, but I'm not sure that's necessary to validate the concept of infinity.

I could be way off the mark though, and maybe this isn't what you meant at all - but at least I'm trying to move this thread beyond the obvious maths.

 

[Nim]

Ok. I have sat through enough spurious arguments and statements that are not so much merely illogical as they are entirely ridiculous. I refuse to subject myself to the same torture as last night, and see so many, many people fly in the face of reason.

I hate myself for doing this, as I normally hate people doing the exact same thing, but could someone tell me if someone has provided at least an attempted rebuttal to Zeno's paradox in the last 20 pages? If, for whatever reason, you feel that the answer to the thread title is 'No', feel free to enlighten yourself about the principles behind this concept, and explain how you have managed to complete a journey in your life.

The sum of an infinitely decreasing series will reach its limit, whether you are looking at it mathematically, philosophically, or sideways through the bottom of the bottle. If you don't believe that an infinite series can exist, then this is not the thread for you. If 0.9r cannot exist, then obviously it cannot equal one, but that is not the point of this thread. The supposition that it is possible to provide a construct for 0.9r is given by the title of the thread. If you want to start a new thread about whether an infinite series is possible, feel free. I won't read it though, since this argument has gone as far as it physically can without causing me to put someone's head through the wall.

In closing...

 

[AlphaNumeric]

Originally posted by Reezer
Any comparison you do with infinity causes big problems because is not possible to evaluate properly.

In respect to 0.9r, infinity isn't a number, its part of an operator. An operator tells you what to do with the number it operators on. "Infinite expansion of decimal" has a well defined meaning, and hence you can evaluate numbers using it.

Originally posted by Reezer
Hell, mathematitions can't even decide what happens when you do the basic arithmetic operations with it. 1/0 = inf? you would think so, but apparently not, inf/2 = ?.... inf?

True, you can't do basic arithmetic like that, hence why "1/0" doesn't exist in mathematics. Its a singularlity. Its not part of the Reals. However, theres loads of stuff you can do as things tend to that value. Entire fields of mathematics (Residue Theory) have arisen to help deal with such things. 1/0 has no meaning, but 1/X, as x-> 0, is a different entity, and provided you don't go completely to x = 0, operations can be done. Google for "Laurent Series", "Residue Theorem", "Contour Integrals" and you'll see what I mean.

Originally posted by Reezer
If top mathematical brains the world over can't devide those things i don't think a bunch of geeks on a forum will be able to answer it

True, but given that they've got well defined, and long standing methods for such things, I'd say they've got such things covered, and those "geeks on this forum" saying otherwise might be wrong, yes?

Originally posted by Reezer
Let's just say for all intents and purposes 0.99r = 1, but technically maths hasn't advanced enough for us to determine the real answer.

Maths advanced far enough for us to reach the real answer by 1750. You're 250 years behind the time. If you studied maths (even at A Level) you'd know maths is way more advanced than worrying about sums of infinite series (especially convergent ones!)

Originally posted by El Gringo
And yet now, it's been accepted that it can also be thought of philosophically. How things change...

Yet it doesn't change the "Mathematically its right" thing though does it? People here have stood up and said "I'm right, you're wrong, Stephen Hawking is wrong, even God is wrong!" There's one thing to be open to say "Mathematically its right, philisophically, well that doesn't prove anything" and another saying even if God himself came down to correct you, you'd still not change your mind.

Originally posted by Haly
The rest I have encountered before but tbh didn't realise it was that high a standard of maths

Vector Spaces is 1st year mathematics. That said, your definition of them is incorrect too. You cannot multiply vectors together in a vector space.

Someone just MSN'd me with a comparision of your quotes and Mathworld's quotes :

Banach Space (exact quotes):
Haly: It's a Complete vector space... can't remember much more
Mathworld: It's a complete Vector space...(goes into notation she wont understand)

Vector Space:
Haly: It's a space where you can add and multiply vectors
Mathworld: Is a space which is [closed under] vector addition and scalar multiplication.....(goes on) (and btw, you cant 'multiply a vector (A-Leel/GCSE knowledge)

Does seem to link up strikingly That and your explaination of Measure Theory is almost a word for word copy of Mathworld too. Scalar multiplication isn't the same as vector multiplication. I don't mean to go OTT, its just its one thing to say "I've heard that word", its another to claim understanding from just "chatting with a professor". I've heard the word "Combinatorics", but I don't understand it (4th year course), but what I've heard is enough to put me off taking it!

 

[n3crius]

.9 recurring is just that. I guess philosophically in theory the number doesn't exist unless you can spend an infinite amount of time writing it out.

Therefore it's never gona be 1 which we can write out in a second.

Mathematically, the number is infinitely close to 1, but will never actually be 1.

 

[memphisto]

alpha this is more of a question than rebuttal to any proof.

but how come the equation only works to prove that 0.99r = 1 ?

what I am getting at is why does 0.88R when put through the same formula not equal 0.8r ? or something close ot it and actually = 1.125 ?

at which point the proof would be thrown out of the window as 0.8r cannot = 1.125 can it ?

yet 0.77R put thorugh the formula = 1.2857 ?

Now I can see with the formula as we go up the numbers from 0.1r to 0.9r the figure starts above 1

x=0.11R
10 x-x = 1

X = 10

see so the formula proves that 0.11R = 10 ?

then as we get closer to .99r that 10 figure drops and drops until eventually we get 0.99r = 1 ?

but if we discount everynumber before that because it is false why do we accept 0.99r= 1 ?

 

[AlphaNumeric]

Originally posted by n3crius
.Mathematically, the number is infinitely close to 1, but will never actually be 1.

You missed the last 27 pages, including mathematically proofs right?

Originally posted by memphisto
but how come the equation only works to prove that 0.99r = 1 ?

x = 0.8r
10x = 8.8r
9x = 8
x = 8/9.

Put in 8/9 in your calculator and you'll get 0.88888....... up until it runs out of screen. Its an infinite sequence of 8s.

x = 0.7r
10x = 7.7r
9x = 7
x = 7/9

Works fine

 

[memphisto]

ahh i see i did it the worng way round was doing 9/8 too little sleep and brain hurting too much i think

I see the error of my ways

 

[AlphaNumeric]

No problem Thats actually the method used to turn any recurring decimal into a fraction (since any recurring decimal can always be expressed as a fraction)

For instance :

x = 0.1421r
10000x = 1421.1421r (10000 used because its 4 digits repeating, not 1, then you'd use 10 )
9999x = 1421
x = 1421/9999

Put in 1421/9999 into your calculator and you'll get 0.142114211421... , repeated till it runs out of screen Its a neat little method taught in GCSE I think, I remember my teacher explaining it at some point.

 

[Deadly Ferret]

Originally posted by Harley
If still in doubt, then on a more general level take a look at Principia Mathematica by Betrand Russelll and Alfred Whitehead for the application of philosophy to mathematics.

Wasn't that book written by Newton?

 

[memphisto]

for some strange and unkoonw reaosn this thread actually had me wanting to retake my A Level maths

but then i realised that the same problem would probably occur as the last time i took A level maths.

I just didnt see any point to algebra

 

[Mozart]

Again, without reading the thread:

0.9r, if you will, defines a system where there is only "9"; there is no space on the end for a gap where you could fit 0.0...1; there is only an infinity of 9s. Because there is no gap, it is fundamentally different to writing a finite number of 9s.

So it refers to the same thing as "1".

If you don't accept that, fine, let the thread die here.

 

[AlphaNumeric]

Originally posted by Deadly Ferret
Wasn't that book written by Newton?

True, but it was also written by those guys too (at a later date )
http://www.thoralf.uwaterloo.ca/htdocs/scav/principia/principia.html

Suffice to say, its not "light reading", its hardcore set theory and logic. Kind of the stuff where its "Assume nothing but the basic axioms, and prove everything". Turns "1+1 = 2 implies 2+1 = 3" into a 10 page proof. Someone gave a "fun lecture" (fun, sure.....) on "How to turn short proofs into long complicated proofs" here in uni last year, and it was based on Set Theory.

It takes 347 pages before that book defines "1", shows how utterly complex it gets.

Originally posted by memphisto
I just didnt see any point to algebra

For 98% of people, they don't need it. Its the 2% that use it to work out how all machines, electronics and the rest of the world works. Its kind of like I don't understand how parts of my car engine work, because I never have to tinker with it. Still, I'm glad theres someone out there who understands it, its quite essential to working cars

 

[Fusion]

Can't believe this is now the 6th largest thread in gd (or that I spent half an hour reading what I'd missed by going to bed early)

 

[memphisto]

Originally posted by AlphaNumeric

For 98% of people, they don't need it. Its the 2% that use it to work out how all machines, electronics and the rest of the world works. Its kind of like I don't understand how parts of my car engine work, because I never have to tinker with it. Still, I'm glad theres someone out there who understands it, its quite essential to working cars

no, Its not that i didnt understand it it sthat I didnt see the point in it, obviously im talking GCSE / early A Level maths but I simply couldnt get over the notion as to why it was useful.

I cant really think of a way of explaining how i felt about it TBH however it goes something like this

Algebra was a shorthand version of working saying a longhanded thing

i.e

speed = distance divided by time

however in algebra it would be s = d - t

or something so I always used to think whats the point why not just write

speed = distance / time ? that way everyone can understand it.


now thats probably not a very good example at all, however its the only way I can think of explaining why I didnt think algebra was useful.

However I know it must be, just couldnt get myself over the why shorten it mentality ?

you know what I mean ?