[split] 0.999... equals 1

[fr0d0]

It's perfectly reasonable and the stance of many mathematicians - check Adrian's last link above! Of course you apply different logic - so bad luck mr bad guy! LOL

[Tiberius]

Yes, we apply a logic which says that P cannot equal ¬P.

[theVOID]

You cannot have both

0.9... = 1

And

0.9... =/= 1

[Edwardo Piet]

You completely miss the point - but you also seem to blindly accept - so really there's no point talking with you. Same with everyone - you're so sure you're right you've given up thinking. As Leo says.. you're spouting theistic crap!

I don't blindly accept, it makes sense. It's not thesitic crap, it applies to everyone, it's logic. It doesn't just apply to theists, and it isn't "crap".

As I said, there can be no gap between 0.9r and 1 so they must be the same number.

At every point along the infinite series, there is a tenth shortfall, infinitely. Maybe it can be written 10-0.1r

But this "shortfall" cannot be any less than 1 at all, because the infinite string goes on forever... so it must be equal to 1. So how is it really a "shortfall" when it goes on for infinity? 0.9r is decimal for 1.

We knot???

I mean't "we know", it was a typo and I think you 'knot' that very well...

How can there be no gap if there's a tenth gap to infinity - you talk shite!

There can be no gap because if there was it wouldn't go on for infinity... if there is a number in-between 0.9r and 1 then it's not 0.9r, it must be less than 0.9r...

What utter tosh Evie! You are the master of misunderstanding. I NEVER SAID I REACHED FUCKING INFINITY! Show me where I did!?!

Did I say you did? I said taht 0.9r doesn't need to reach 1 because it is 1, whereas you said that it can "never reach", but it is not supposed to. I don't believe I said that you said that it can 'never reach infinity itself'?

Read the fucking words and come back to me if you have a fucking point - stop wasting my time with your fucking misobservations all the time!!!

Re-read what I said because it seems you 1. Misrepresented me, 2. You still don't get it, and 3. You still don't get it and the logic of it, despite the fact that I thought you said you did after Adrian explained it to you ages ago?

0.9r and 1 'converge' only in the sense that they are the same number, represented differently... because 0.9r cannot be any less than 1 because there can be no gap between the two otherwise it wouldn't be 0.9r, the 9s on the end - recurring - wouldn't be going on and on forever and ever.

I'm not talking about infinity as a whole, but the journey to infinity, which we can see by the progression of 9's, follows a pattern of 9/10ths of the whole... infinitely.

And if it goes on forever, how can you fit a number between it and 1? What number can never be between 0.9r and 1? There logically can't be a number between them, or it wouldn't be 0.9r (see above).

As we know the pattern MUST stay at 9, we can know that it will never converge

It doesn't need to converge or 'reach it', because when it goes on forever it logically is 1, it doesn't need to converge. 0.9r represents 1 in decimal because there can be no gap between it and 1, so it's 1... no number can fit between it.

I thought my analogy was a good one, and I'd like to see a sensible explanation of why it isn't correct.

Because this is not about 0.9r having to reach 1, this is about how 0.9r logically is 1, represented in decimal... exactly 1, because there is no number that can be between it and 1, so it logically is 1 (in decimal). It's just counter-intuitive, but once you've got it you've got it, because it makes perfect sense.

EvF

[Ephrium]

EVF, your logic is flawed.

In the discrete number system, there is no number btween 5 and 6, but are they equal?

But I believe 0.9r =1

[Rhizomorph13]

What about 5.1? lol

Rhizo

[fr0d0]

Indeed Evie, your logic is flawed. The reality is like I said. Some say 0.9... = 1 and that is an assumption.

[Meatball]

I think it might be better to use 'there exists no number that you can add to .9r such that the result is 1' than 'there exists no number between .9r and 1'

• For every x and y, where x and y are real numbers and x < y, there exists a positive real number, z, such that x + z = y.
• There exists no real number that you can add to .9r such that the result is 1, and vice versa
• Therefore, we can conclude that .9r = 1.

Any of the deniers in this thread, feel free to show me a value of z that breaks this argument. If .9r is so obviously a lesser number than 1, it shouldn't be a big deal, right? So what is it?

For all the beans: 1 - .9r = _____

[Tiberius]

It is only an assumption if you count every branch of mathematics as an assumption also, and if you did that, the problem becomes meaningless since every number is only an assumption itself

[Edwardo Piet]

EVF, your logic is flawed.

In the discrete number system, there is no number btween 5 and 6, but are they equal?

But I believe 0.9r =1

There are many numbers between 5 and 6.

For example: 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 57. 5.8, 5.9 and all the decimals in between.

Unlike 0.9r where there literally can't be a number between it and 1 otherwise it wouldn't be 0.9r.

Indeed Evie, your logic is flawed. The reality is like I said. Some say 0.9... = 1 and that is an assumption.

What Rhizo said and what I said gave proof that this is nonsense.

There is a difference between there being a number between 5 and 6 and a number between 0.9r which has 9s that go on for infinity! What number could you fit between?! 0.9r can't have numbers in between or it wouldn't be 0.9r, unlike 5 and 6 which you can of course have numbers in between.

EvF