Guess that approximation can be done.......]]>

I'm good too.

You wrote:

and those aren't two numbers in actual sense .........

because pi is a symbol that is used to represent a particular decimal,3.1415.........

But my point (see also earlier comments by me) is that all numbers are like this.

"1" is the symbol I use to represent the decimal 0.999999.....................

Bob

]]>What I was disagreeing with is

0.999... + 1/∞ = 1

'm good and how are you doing.....???

and those aren't two numbers in actual sense .........

because pi is a symbol that is used to represent a particular decimal,3.1415.........

Hello Bobbym;

almost the whole of the argument you were trying to prove that .999999...... isn't equal to unity

that is what i actually agreed on..........

hi Maiya

Haven't heard from you for a while, how are you?

I think you can have two numbers that are the same like this

Bob

Pi isn't exactly equal to that, the decimal is an approximation. So you should not put a "=" sign, you should put "≈"

]]>i totally agree with Bobbym...

Not exactly, half the time I do not even agree with him but he makes a good bowl of soup.

If you become convinced .999999... = 1 then you totally agree with bobbym.

ncik wrote:

Also, the sum from n=1 to infinity of 9(1/10)^n = 1. But that's beside the point and not a very intuitive proof.

I would rather say .9999999... = 1 and be able to continue using the sum of a geometric series formula then not.

]]>And 0.9999999999999.....can never be equal to unity.....

limit of .999999..... could be 1

but saying that .99999999...itself is equal to 1 would be absurd since both of those numbers have their own existence which cannot be equated......

It is just another way of saying the other. An endless number of 9's just mean the same thing as the number of 9's approaching infinity.

]]>Haven't heard from you for a while, how are you?

I think you can have two numbers that are the same like this

Bob

]]>i totally agree with Bobbym...

since infinity is no real number and since its value is not known,arithmetic of infinity cannot be performed as we do in case of other numbers.....

And 0.9999999999999.....can never be equal to unity.....

limit of .999999..... could be 1

but saying that .99999999...itself is equal to 1 would be absurd since both of those numbers have their own existence which cannot be equated......

Excellent points. And totally relevent. If mathematicians want to give a meaning to 0.9999..... then it is essential to consider what properties it would have. Once 'you' have a water-tight definition it is 'safe' to go ahead and define what it means, knowing that there are no chinks where someone can drive through an objection.

Bob

]]>Also, the sum from n=1 to infinity of 9(1/10)^n = 1. But that's beside the point and not a very intuitive proof.]]>

but it's generally accepted that 0.999... + 1/∞ = 1

Not by number theorists. The rules (axioms) for number theory specifically do not allow infinity to be treated as a number. It doesn't obey the rules of arithmetic so 1/∞ is meaningless.

You can make up a mathematical system which uses the infinity symbol:

eg.

∞ + 1 = ∞

∞ + ∞ = ∞

and so on,

but this is NOT number theory and is usually avoided by mathematicians.

In the context of the discussion about 0.999999 recurring and 1, it is not appropriate to use ∞ as if it were a number at all.

Throughout I have said you can define numbers to mean what you want so you might think that allows someone to define ∞ as a number.

But you have also to show your definitions pass the 'consistency test'. ∞ as a number does not.

Background reading: such as

http://www.calvin.edu/~rpruim/courses/m … nt-pp4.pdf

Note axiom 7.

Bob

]]>I don't know how to put this in a way you can understand, but it's generally accepted that 0.999... + 1/∞ = 1

That is not generally accepted because of a couple of things, for one 1 / ∞ ≠ 0.

We could say

but that is not the same thing.

This is also a little funny

0.999... + 1/∞ = 1

you can not use infinity as if you were using the number 5 or 56. Infinity is not a number. You can not do arithmetic with it. It would lead to many contradictions.

What is true is

1 / 3 = .3333333...

you need nothing else notation wise. Now just drop the 1/∞ from your thoughts and you are there. We both can then agree

1 / 3 = .33333333...

3 ( 1 / 3 ) = 3 ( .3333333....) = .99999999...

1 = .99999999....

Now we can start to do some mathematics! We agree with everyone else about the rules of the game.

Base 10 isn't perfect cause it's a round number.

Base 10 is a positional number system that uses powers of ten and the digits 0 - 9 to represent numbers. It is a not a round number nor is it flawed.

]]>0.999... + 1/∞ = 1

(0.999... + 1/∞)/3 = 1/3 <- Divide both sides by 3

0.333... + (1/∞ * 1/3) = 1/3

0.333... + 1/(∞*3) = 1/3 <- Simplify (1/∞ * 1/3)

So to sum this up in words:

A third is equal to point three repeating plus a third of an infinitesimal, which sounds absurd, but it's true. Base 10 isn't perfect cause it's a round number. There's always a flaw. But it's too late to change number systems easily, so we just have to deal with these flaws.