Is 1 = 0.9999......

[MadRat]

Originally posted by: josphII
i=sqrt(-1) is not an argument, its fact

[edit] fact isnt the right word, i=sqrt(-1), by definition, not by argument

Imaginary number

An imaginary number is a number whose square is negative. The term was coined by René Descartes in the seventeenth century and was meant to be derogatory: obviously such numbers don't exist. Nowadays we find the imaginary numbers on the vertical axis of the complex number plane. Every imaginary number can be written as ib where b is a real number and i the imaginary unit with the property that "i^2 = - 1".

Cogito ergo sum

 

[Haircut]

Originally posted by: MadRat

Originally posted by: Haircut
I ask you again, what is the infinite digit?

I could presuppose you mean something else. I'll let you explain what you want for an answer.

Well, you're the one who thinks this infinite digit exists.
If, as you said earlier that the infinite digit is 'the same fraction that formed it' then what about when we want to know the infinite digit of an irrational number.

What is the infinite digit of 0.12112211122211112222...
or perhaps the infinite digit of Pi, or sqrt(2). If you are so intent on beliving the idea then surely there must be a way of knowing what it is?

 

[MadRat]

I said a value can exist in the infinite position. Big difference.

 

[Haircut]

Originally posted by: MadRat
I said a value can exist in the infinite position. Big difference.

How can it for an irrational number though?

The decimal expansion of an irrational number is always nonterminating (it never ends) and nonrepeating (the digits display no repetitive pattern).

Also, do you have any evidence for this concept of a value at the infinite position? I am open to new ideas, and if you provide some mathematical evidence (other than yourself saying it exists) then I might be inclined to take you more seriously.

 

[MadRat]

I gave you a hint in my second to last post.

 

[josphII]

Originally posted by: MadRat

Originally posted by: josphII
i=sqrt(-1) is not an argument, its fact

[edit] fact isnt the right word, i=sqrt(-1), by definition, not by argument

Imaginary number

An imaginary number is a number whose square is negative. The term was coined by René Descartes in the seventeenth century and was meant to be derogatory: obviously such numbers don't exist. Nowadays we find the imaginary numbers on the vertical axis of the complex number plane. Every imaginary number can be written as ib where b is a real number and i the imaginary unit with the property that "i^2 = - 1".

Cogito ergo sum

your point?

 

[Haircut]

Originally posted by: MadRat
I gave you a hint in my second to last post.

Jeez, the way you avoid actually answering the question you should become a politician.
As far as I can see your second to last post does not hint anywhere towards the idea that there can be a value at the infinite position.

Please, either show a flaw in one of the proofs of 0.999... = 1 or provide some mathematical backing to the idea of an infinite position in a decimal expansion.
Your 'it's well known' won't cut it.

 

[josphII]

what i would like to see is a reference to a math book that lists 1/3 != 0.333... as madrat claims, or even a reference that 0.999... != 1

 

[spyordie007]

Originally posted by: MadRat
I said a value can exist in the infinite position. Big difference.

Madrat-

There is no such thing as the "infinite position", mearly mentioning that you think such a thing exists is another indication of the underlying problem you have with understanding the simple fact that ".999*" is equal to "1".

I also get the feeling that you are arguing with everyone here simply because you want to argue, if that is the case I have a picture for you.

-Spy

 

[RossGr]

The notion of a digit in the "infinite postion" is nonsensical. To speak of a digit of a real number implies that it holds a specific postion in that number, as soon as you pick a digit its location can be specified by some initeger N, therefor it is not "at infinity" but in the "Nth" slot. It must be followed by an infinite number of digits, if the number is infinitly repeating, or Irrational.

 

[Kyteland]

Originally posted by: MadRat

The personal attack means you've ran out of argument, eh? Fine, I won. Now apologize like a man.

The chilish retort means you've run out of arguments, right? Fine, I won. Now grow up and act like a man.

You seem to fall back on this argument a lot, but it sounds like a case of "I know you are but what am I?" to me.

 

[Kyteland]

Originally posted by: heliomphalodon

It would make just as much (actually, as little) sense to have a poll on whether "1+1=2" is a true statement.

Actually, 1+1=3.

(For large values of 1 and small values of 3 )

 

[bleeb]

0.9999.... != 1

 

[TuxDave]

Originally posted by: bleeb
0.9999.... != 1

dieeee... 0.9999..... = 1

 

[Kyteland]

Originally posted by: bleeb

0.9999.... != 1

You know, this thread might actually die if you'd just let it.

 

[Darien]

Originally posted by: TuxDave

Originally posted by: bleeb
0.9999.... != 1

dieeee... 0.9999..... = 1

Sigh...here we go again...

 

[bleeb]

Lets not lead this profound thread die. Lets keep it going!

I still believe that 0.9999.... != 1

 

[MadRat]

I'm still waiting for these guys to prove that no value can exist at the infinite position. So far they just say it cannot.

They can only detract from the argument with distractive mutterances about their higher learned level arithematic degrees that may or may not exist if we really cared.

 

[TuxDave]

Originally posted by: MadRat
I'm still waiting for these guys to prove that no value can exist at the infinite position. So far they just say it cannot.

They can only detract from the argument with distractive mutterances about their higher learned level arithematic degrees that may or may not exist if we really cared.

Ok, I'll try my best on that one. I say it can't exist because it doesn't make sense if it did. For instance, I'm ASSUMING that pi has an infinite number of digits after it to represent the value. (I'm not sure, but it's the best I can do). If a digit can exist at the infinite place, then there does exist a last number to pi right? Does that make sense? Does it make sense to claim that an infinitely long stairway has a top? If you think so, then this becomes a philosophy of math debate.

-Dave-

 

[bleeb]

Think of it this way... okay so you have this term "Infinity," which I'll denote as INF. Now the definition of INF is:

Mathematics. The limit that a function is said to approach at x = a when (x) is larger than any preassigned number for all x sufficiently near a.
(Dictionary.com)

Using this definition... they are saying that INF is the limit at which f(x) approaches when x is larger than any preassigned number, which they [dictionary.com] define as 'a'.

Now if you assign the largest number to x (INF) then you can still find a larger number by the above definition for f(x). but by being able to assign a larger number to this number you are going against the very definition which was defined. So with that conjecture, you say that as 0.9999... = 1, they are in fact saying that you can find a larger number for x that is greater than infinity and greater than the limit of f(x=infinity). Therefore you will NEVER reach 0.9999... = 1 since you could never reach infinity because you will always be able to define a number value of X which will be greater than the greatest defined number.

In summary 0.9999... != 1.

 

[silverpig]

Originally posted by: bleeb
Think of it this way... okay so you have this term "Infinity," which I'll denote as INF. Now the definition of INF is:

Mathematics. The limit that a function is said to approach at x = a when (x) is larger than any preassigned number for all x sufficiently near a.
(Dictionary.com)

Using this definition... they are saying that INF is the limit at which f(x) approaches when x is larger than any preassigned number, which they [dictionary.com] define as 'a'.

Now if you assign the largest number to x (INF) then you can still find a larger number by the above definition for f(x). but by being able to assign a larger number to this number you are going against the very definition which was defined. So with that conjecture, you say that as 0.9999... = 1, they are in fact saying that you can find a larger number for x that is greater than infinity and greater than the limit of f(x=infinity). Therefore you will NEVER reach 0.9999... = 1 since you could never reach infinity because you will always be able to define a number value of X which will be greater than the greatest defined number.

In summary 0.9999... != 1.

You've got it pretty much right, except for you have to understand that the definition of 0.9... is that the nines are already infinite.

 

[Dufusyte]

1/3 does NOT equal 0.3333333...

because you cannot write an infinite string of 3's.

A "repeating" number is not a number at all. It is a process, indeed, it is a process without termination.

Therefore "0.999999..." is, likewise, not a number, but rather a process without termination.

Notice that we have to write dots at the end of it to symbolize the fact that it is a non-terminating process. Similarly, if we write it with a superscript Line over the 9, the line indicates that it is a non-terminating process, and not a rightful number.

So "0.99999..." does not equal ANYTHING, since it is not even a fixed number itself.

It is a process whose numerical value lies between the point where you leave off the process, and 1. For example, if you write it as "0.9...", then its value lies between 0.9 and 1. If you write it as "0.99999..." then its value lies between 0.99999 and 1. Please note: the value NEVER reaches 1, no matter how long you extend the process.

Therefore, to the people who say:

1/3 = 0.3333...

I reply, no, 1/3 does not equal 0.3333...

In truth, 1/3 can only be expressed as a fraction. It *cannot* be expressed as a decimal. If you try to express it as a decimal, you run into an interminal process, and the numerical value of the interminal process will lie between the point where you leave off the process and 1/3, but it will never reach 1/3. So it is erroneous to say that 1/3 = 0.33333..., and hence the rest of the proof fails as well.

Hence, the "proofs" advanced in prior posts are shown to be in error.

Quod est demonstratum.

 

[TuxDave]

Originally posted by: bleeb
Think of it this way... okay so you have this term "Infinity," which I'll denote as INF. Now the definition of INF is:

Mathematics. The limit that a function is said to approach at x = a when (x) is larger than any preassigned number for all x sufficiently near a.
(Dictionary.com)

Using this definition... they are saying that INF is the limit at which f(x) approaches when x is larger than any preassigned number, which they [dictionary.com] define as 'a'.

Now if you assign the largest number to x (INF) then you can still find a larger number by the above definition for f(x). but by being able to assign a larger number to this number you are going against the very definition which was defined. So with that conjecture, you say that as 0.9999... = 1, they are in fact saying that you can find a larger number for x that is greater than infinity and greater than the limit of f(x=infinity). Therefore you will NEVER reach 0.9999... = 1 since you could never reach infinity because you will always be able to define a number value of X which will be greater than the greatest defined number.

In summary 0.9999... != 1.

Plus we are not doing a limit, we are starting at a pre-existing number denoted as 0.9999.... and given that we start there, is that equivalent to 1?

 

[TuxDave]

Originally posted by: Dufusyte
1/3 does NOT equal 0.3333333...


Quod est demonstratum.

More like circular reasoning. You already redefined 0.999... to be a value less than 1 by making the statement that the process of 0.9999.... will lie between 0.9999 and 1. This forces 0.999.... to be less than 1, which is the definition to which we are arguing. But GIVEN that, then your proof is true, but your proof was to prove what you took as a given. Circular reasoning?

 

[RossGr]

Dufusyte
Are you trying to tell me that I am not allowed to even think about a real number which contains an infinatly repeating sequence of digits. Is there some law that you passed? I missed it, should I turn myself in to the thought police because I CAN think of this real number which I cannot write out explicitly. Why is it not permitted to write it symbolically? Tell you what, the number 10^ -(10^100) has a bunch of zeros followed by a one, I have not written them all out, I will go so far as to bet the NOONE has EVER written that number down, by your logic it does not exist. Seems to me we have a problem here, is it necessary to write down a number before it can become "real".

I am sorry your artifical requirement that you must be able write a number down simply does not hold water.
so .333.... = 1/3 and .999.... =1

If anyone wishes to shoot down a proof you must address the one I have written it is linked to several times in this thread but just to make it easy here it is again. Note that this has been updated since my original post and now does not containt the typos. In additon I have inculded a definition and proof of the meaning of equality in real numbers. Please address this proof if you wish to claim .999.... !=1.