9/9 ?????????????????????

I'm trying to be polite and not just come out and say, "Fox, that is bull****."

Opps.. I just said it.

Honestly... math is self evident. Man didn't "invent" it. Time is self evident. Man didn't invent that either. If we weren't around, it would still pass. If we weren't around, you could still observe 1 tree on the beach and a billion stars in the sky.

We only invented the words, the names we placed on each value. We invented the word, "one". We didn't invent the value. We invented the word "plus". We didn't invent the operation. One plus one equal two. That is self evident. If you have one rock, and you drop a second rock beside it, you have two.

1 + 1 = 2
one plus one is two
un plus un est duex
. U . E ..

All of that says the same thing. It doesn't matter what I call it. Math is self evident. Man didn't invent it.

B is Prime! B is the same as 11. Both are prime. It doesn't matter what base I put it in, it doesn't matter what I call it, they are prime. That is a mathematic, self-evident principle. No one needs to have observed it for it to be true. It is. No one invented the idea of prime numbers, they just named them.

Your arguement is flawed.

Guv.

I didn't just say there has to be a real number between the 2. I said there must be a Terminating decimal between the 2.

0.99... is a non-terminating decimal. there is no finite value of N whereby 0.99... = Decimalseries(N)

so you can't use HexidecimalSeries(N) because that's a non terminating decimal also.

Quote:

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Originally posted by kedaman

also everything is being defined by human, oh yeah and if you want to apply something on reality, go find it first. Good explanation fox :)

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Kedeman. Can you find gravity? Not the existance of it, but can you find it?

No, neither can I. But you know something. It exists. No one invented it. It was there before man, it will be there after man. Gravity exists and no one can find it.

:) Don't hop on Fox's wagon, its missing a wheel.

CyberThug.

We're not talking about gravity or space or anything, we're talking about numbers. Man invented Numbers, and has now defined them with about 10 axioms from which everything else is proved. including that 0.99... = 1.

Crazy people, with crazy talk.

Man didn't invent numbers. Man invented a system to express self-evident mathematical laws. 1 + 1 = 2, that is real. Man didn't invent the principle behind that, just the means to express it.

And because man invented a means to express it, that means is flawwed. That means falls short of expressing it in its true form. Which is why:

0.999... is an underflow approximation of 1 because your proof, while correct in its logic, is severly flawwed in its assumptions!

It assumes that a<b<c where b has to be a terminating decimal. I don't see any reason why it has to terminate.

Your proof hinged on that being true, and when it is not, your proof is meaningless.

And... yes, we are talking about space and rocks and trees and everything, because we are talking about math. Without math, there is no everything.

Self evidence doesn't explain anything, in fact since the first human has born (if that ever has) they had to invent every single axiom. That doesn't just apply to math's or physics, we are a bunch of genetical interpretors of stored axioms of who knows what.

If you try to find reality, you won't. You won't believe me either but you won't come up with a proof againt me.

math was invented to describe what we call "reality"

And since nothing exists all these arguments are worthless if they require "reality" to be valid :p

Quote:

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Originally posted by kedaman
Self evidence doesn't explain anything, in fact since the first human has born (if that ever has) they had to invent every single axiom. That doesn't just apply to math's or physics, we are a bunch of genetical interpretors of stored axioms of who knows what.

If you try to find reality, you won't. You won't believe me either but you won't come up with a proof againt me.

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I'm going to politely ask this...

What are you trying to say?

Man invented what axioms? There are genetical interpretors for what?

Look... watch this...

11 is prime. If man invented that, then it is only true for man. We go out into space and we find Notman, a race of aliens. Guess what... they have a number in their base 7 system (since they only have 7 fingers) that is prime, too. They don't use the word prime, but after we translate it, we understand. The 11th positive in their number system is prime.

Is that a coincidence? According to you, we invented our numbers. They must've invented theirs. But how did we both invent the same prime?

We didn't! 11 is prime, it doesn't matter how to represent it. It is self-evident.

What self-evident means is... if a tree falls in the woods, it makes a sound, even if no one is there to hear it.

11 is prime, even if no one was ever born, anywhere.

nope it requires a human for it to be valid :p

Quote:

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Originally posted by kedaman
nope it requires a human for it to be valid :p

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Oh, I get it. You are just joking, just pulling my chain.

Man... I was getting so worked up thinking that you were really that thick headed.

I mean, anyone who has gone through freshman calculus has to realize that man didn't invent prime numbers or any part of math. Hell, just watch First Contact (or read it if you can wade through Sagan's socio-political commentary).

That's Contact.

First Contact is the Star Trek film :)

D'oh!

My bad.

Contact by Carl Sagan, with Jodie Foster.

Pretty good film, it was on a few months ago :)

those "Notmans" may exists only in your mind.
you probably didn't understand the point i was making.

Pick a formula for instance newtons for gravity F=ma. does it apply on "reality"? usually, but not always, in some cases you need take in aspect the relativistic mass and length. Each time you pick a formula, which applies on what you interpret, so that you can feel the satisfaction of having "correct" results. Now this is something you, apply yourself, but mostly it isn't even your choise. Who choosed you to not be able to see infrared or ultraviolet? Why do you feel cold when less particles are bombarding you, why do you die?

Genetical axioms, such you have been provided with. Now you can't distinguish between what is real and what is not, in fact, you have to define what is "real" and sometimes you have to redefine, most of because the inaccuracy of your genetical or psycological functions.

talking about functions, if you use an api function which returns a value, do you really know what is behind it? what is it really doing behind the scenes?

You don't know, and my point is you won't find out either the essence of reality.

So we have to, and are relying on formulas and models

No joke this time, I'm serious

I didn't think F=ma was gravity, but we will go with it.

Okay... we have a function. According to Fox, we invented this. We created this function. We created the numbers and the fact that when you have a mass of 7g over a distance of 2m per second squared you get a force of 14N.

Guess what... we didn't invent that. And that exists even if we aren't around. That is reality, we just observed it.

8/9 is reality, we just observed it. 9/9 is reality, we just observed it. Problem is... our measurements, our method of expressing it falls short of reality. 0.999... is not equal to 1. 9/9 equals 1, not 0.999....

We can not correctly express a non-terminating decimal. Its behaviour is its own. We just can't show it correctly with out methods.

The thought experiment with the Notmen was to demonstrate that we didn't invent math. It is part of reality, and it is the same reality, regardless of how you observe it or express it. No matter how to slice it, quantify it, if you have this many rocks

* * * * * * * * * * *

then you will find that you can not even split that number into any number of groups.

But if you have this many rocks

* * * * * * * * * *

Then you can split it into even groups.

* * | * * | * * | * * | * *

or

* * * * * | * * * * *

That is not an axiom we invented, that is a fact of reality. If there was such a thing as God, then that is a law that he sat down. And all laws created by god are enforced, even if we don't know what they are.

Oh god.

I did not assume that for any real numbers a and b where a<b there must exist a terminating decimal c such that a<c<b.

I Proved that for any real numbers a and b where a<b there must exist a terminating decimal c such that a<c<b.


Please, go and find an assumption I made that you disagree with and I'll prove it from the basic axioms. but considering that 80% of my post was taken up with a proof of the statement you claim is invalid I think you're being a little unspecific.

Quote:

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Originally posted by CiberTHuG

Guess what... we didn't invent that

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sometimes you take something for given, and sadly, you have to.

Quote:

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And that exists even if we aren't around.

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have you tried?

Quote:

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That is reality, we just observed it.

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observed? can you explain observed to me?

Quote:

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Originally posted by Sam Finch
Now define a number N = 2^p * 5^q
where p and q are positive whole numbers and N > 1/(b-a)

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Okay, I misread your proof. Now that I look over it again, I like it even less.

I can't find positive whole numbers for p and q such that N will be greater than 1/0.000...001.

Which just proves my point (pun intended). 0.999... is an underflow approximation. It is fine to say 0.999... is equal to 1 when you work with things like the following...

1/9 + 8/9
0.111... + 0.888...
0.999....

But you have to keep in mind, there is a singular point that seperates the two. Otherwise, anytime you took the limit of something you could say that foo is equal to bar as opposed to foo approaches bar.

Your proof is nice, and I use it as a self-test on the system. The system is now aware that it is itself, flawwed.

Kedeman is venturing into semantic and philisophical debates. While i find his tenacity amusing, I see no need to try and show the light to the blind.

You can wax semantics all you want. And since I think the church gives meaning to peoples otherwise dreary lives, I'm not prepared to disprove the existance of god, so I don't care to engage anyone in a philisophical debate.

:)

'Course, I suppose that someone like yourself doesn't believe in a god, anyway, since you have the pride enough to believe man invented math and the reality around him. So I wouldn't be telling you anything new.

ignorance is a bliss right?

ok, these are two very fundemental axioms.

for any real number x where x>0 1/x is a real number and x>0.

for any real number y there exists a natrual number n such that n>y.

and it's not too difficult to show that there's also a natrual number n in the form 2^p * 5^q. (2^n would do.)

if you want to dispute one of these feel free to go along to the nearest university and take it up there, but I warn you they won't take too kindley to you asking them to re-write all the maths books because you've decided that they're wrong.

I sure hope so, Kedeman.

so you don't want to proove me wrong?

Quote:

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Originally posted by Sam Finch
and it's not too difficult to show that there's also a natrual number n in the form 2^p * 5^q. (2^n would do.)

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I believe such numbers exist. But... what is 0.000....001?

I wrote it down, so it must be a number. And I can produce this number:

1 - 0.999...

So what is that number? I'm just trying to look out for that little number.

Now...

if your reality is true, then for y = 1/x, y is equal to 0 for very large x.

Hmmm... that bothers me. That bothers me a lot. And I know it bothers the academic sector. Y is not equal to 0, it approachs 0, but it is never equal to zero.

For the very same reason behind that, 0.999... is not equal to 1. It approaches one, but it can not equal.

Now, you can say they are equal, so long as you understand you are approximating.

Quote:

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Originally posted by kedaman
so you don't want to proove me wrong?

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Well, just because I know that knowledge is not bliss, doesn't mean I can prove that ignorance is or isn't bliss.

that was a qwestion, i was refering to my earlier statement, there's no known reality to refer to. You define it, sometimes whether you want it or not.

still as serious as before.

*grumblegrumblegrumble*

Okay, Kedeman.

I have this many rocks on my desk...


* * * * * * *

I can't split that number of rocks into equal portions for any number of people (save # # # # # # # many people or # many).

Show me where I created the reality, where I affected it?

Sam: The part of your proof that I disagree with is the following.

Quote:

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So if 0.9... < 1 there must exist a non recurring decimal c such that

0.9.... < c < 1

clearly this is not the case so 0.9... = 1.

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How can you assert without proof that there is no such number? It does not exist because you do not know what it is? It does not exist because I cannot specify what it is?

I gave a valid proof (see below) that recurring .9999 is less than one. That proof in conjunction with the first part of your proof proves that there is a nonrecurring number between recurring .9999 and one. To avoid the necessity of hunting through previous posts, an abbreviated version of my proof is as follows.

• DecimalSeries(N) = 9/10 + 9/100 + 9/1000 . . . + 9/10^N
• HexSeries(N) = 15/16 + 15/256 + 15/4096 . . . + 15/16^N
• DecimalSeries(N) < HexSeries(N) < 1 for all values of N.
• Hence there is a value between DecimalSeries(N) and one.
• Therefore DecimalSeries(N) not equal to one for any value of N.
• DecimalSeries(N) is a formal representation of recurring .9999
• Hence recurring .9999 < 1

It is true that the limit of both DecimalSeries(N) and HexSeries(N) is one. It is also true that DecimalSeries(N) is not equal to HexSeries(N) for any value of N, nor is it equal to one for any value of N.

One should not confuse a function and its limit. A proof involving a limit merely proves that some function gets arbitrarily close to its limit. Such proofs never prove nor assert that the function ever equals its limit.

In many contexts, it is valid to use a limit in place of the function. This is a matter of notational convenience and merely indicates that for practical purposes, the limit can be used instead of the function. Such usage does not imply that the limit is theoretically equal to the function.

Such usage of a limit in place of a function leads to posts such as this. Of course 9/9 = 1. To think that it equals recurring .9999 is theoretically absurd, but true for all practical purposes (If you ignore the wastage of printer’s ink and space on a page).

you are assuming so much again, i guess i could put up a list of millions of Why...? What...? How...? and you won't be able to answer none of them, if you try, you will find out there's a border you can't pass, that your knowledge is limited and that you can't distinguish reality.

for instance, "split" is a function we apply in several models, if you define one of them with reference to reality, you have prooven me wrong, go ahead.

Kedaman, who are you responding to?

Guv, very nice job. I don't think I said so earlier, but very pretty.

you of course :)

Guv, did you notice that

these:

DecimalSeries(N) = 9/10 + 9/100 + 9/1000 . . . + 9/10^N

Therefore DecimalSeries(N) not equal to one for any value of N.

doesn't match

0.99...

because if you put a value N you have a value with a specific amount of decimals, that is N

Quote:

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Originally posted by kedaman
you are assuming so much again

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What am I assuming? WHAT??? If you can't name it, then is it really so?

Quote:

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, i guess i could put up a list of millions of Why...? What...? How...? and you won't be able to answer none of them, if you try, you will find out there's a border you can't pass, that your knowledge is limited and that you can't distinguish reality.

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what the **** are you talking about?

Quote:

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for instance, "split" is a function we apply in several models, if you define one of them with reference to reality, you have prooven me wrong, go ahead.

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Split? What the **** does split have to do with any of this? We are talking about numbers!!! wait.. I'll define sum() if you'd like!

Take a hand full of rocks and put them on the table.

Now take another hand full of rocks. Put them on the table.

You have just summed rocks.

NOW IF YOU WOULD KINDLY STOP WITH THIS RAMBLING CRAP AND EXPLAIN YOUR POINT!!! WHERE DID YOU AFFECT REALITY WHEN YOU SUMMED ROCKS???

I maintain that you didn't affect reality, at all. That the mathematics behind the summation of those two groups of rocks is purely a self-evident thing for which man has labeled... 1 + 1 = 2.

And I just proved it by putting rocks on the desk!

Quote:

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Originally posted by kedaman
Guv, did you notice that

these:

DecimalSeries(N) = 9/10 + 9/100 + 9/1000 . . . + 9/10^N

Therefore DecimalSeries(N) not equal to one for any value of N.

doesn't match

0.99...

because if you put a value N you have a value with a specific amount of decimals, that is N

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Damnit, Kedaman, you are pissing me off.

DecimalSeries(N) = 0.999... where N is equal to infinity.

What was so ****ing hard about that.

i picked "split" of two reasons, one because you mentioned, two because it's the best shortcut to the border i mentioned.

oh btw i saw that, infinity is not a number so you can't put it in N's place.

now if you calm down, we could talk more seriously.

Okay, I don't know where I mentioned split. And I don't care about shortcuts to borders ???

The point behind this whole arguement is wether or not infinity exists. So, you can put it in N's place. If you can't, then... why not say as N approaches infinity if that will make you feel better.

Now, for the last time.

Look over my examples. Where did I affect reality? According to you, I'm making this **** up. But every time I ask you to show me where, you simple say, "You can't understand it."

You know that is no way to prove anything.

Now, don't say another word until you show me where I affected reality.

Quote:

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Originally posted by CiberTHuG
The point behind this whole arguement is wether or not infinity exists. So, you can put it in N's place. If you can't, then... why not say as N approaches infinity if that will make you feel better.

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we weren't actually arguing about that, but i guess we could allow some "multithreading". If N approaches infinity, the series approaches 1.

Quote:

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I can't split that number of rocks into equal portions for any number of people

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here's your statement. and you are assuming split as a function which we implicitely declare and hence risk ambigueties.

Quote:

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Okay, I don't know where I mentioned split. And I don't care about shortcuts to borders ???

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I would because this is already getting boring.

Quote:

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Look over my examples. Where did I affect reality? According to you, I'm making this **** up. But every time I ask you to show me where, you simple say, "You can't understand it."

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I'm trying to avoid things that happened between me and Gen-x. To spawn several issues at the same time doesn't lead anywhere.

Quote:

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You know that is no way to prove anything.

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i hope you know what you are saying.

Quote:

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Now, don't say another word until you show me where I affected reality.

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i am trying, now please give me a chance.

Perhaps there are answers to these questions, it's just possible (nay, probable) that the human brain cannot comprehend at this stage of evolution.

Maybe we haven't been exposed to the right stimuli so far to answer these questions.

Maybe we're at the point of the blind man who is trying to understand the colour green.

We can handle it, yet it's beyond us - if you see what I mean....


PS - Ciber,

I'd lay off Kedaman if I were you. He's one of the most respected people in these forums and it's for a reason.