Is 1 = 0.999... ? Really?

Ok, we’re going to dig at each other every so often, so I’ll just ignore your post after this.

So…

I found it interesting that you omitted the sequence:

1/10+1/100+1/1000+1/10000 etc…

But just decided to write 0.111…

The first part IMPLIES the sequence!

1/9 is finite in that it is a rational in its fraction form!!

0.111… is a repeating rational in its decimal form.

All of this shit:

1/9

0.111…

1/10+1/1000*1/1000 etc…

All equal each other!

I have no clue why you are playing such subtle word games that don’t change the content of what I wrote whatsoever, but here you are, doing just that!

That’s not a sequence, that’s a sum. You are confusing the two.

(0.111\dots), which is the same as (\frac{1}{10} + \frac{1}{10^2} + \frac{1}{10^3} + \cdots), is an infinite sum. It is not an infinite sequence. There’s a huge difference between the two.

It’s not a finite sequence. It’s not a sequence. It’s a NUMBER.

That would be you.

You need to learn language.

It’s only an infinite sum if it converges, an infinite sequence is just an infinitely expanding discernible pattern.

I’m aware that 1/9 is a number. I stated that it’s a rational in fractional form. Because there’s a divisor, it’s also an operation.

Again! You’re playing word games instead of addressing ideas.

Not really.

An infinite sum is simply a sum cosisting of an infinite number of terms. Whether it converges or not has nothing to do with it.

But you don’t seem to be aware that it is not a finite sequence.

Actually, it is you who are 1) playing word games, and 2) avoiding addressing other people’s claims.

As for me, I think I responded to almost every claim you made. Can you show me a claim I did not respond to?

Perhaps you simply don’t like how I responded to your claims? If this is the case, can you explain why? What exactly are your expectations?

Dude, Magnus! Honestly!

“It’s a SUM with an infinite number of terms!! That’s what convergence fucking is! A fucking SUM!!

Not a sequence, not a series! It’s a fucking SUM! A SOLUTION to the fucking additive infinite series!

You never addressed the argument that proves infinite and finite behave differently in anything resembling a rational manner.

It is a mathematical FACT that when you remove something (and notice when I pointed out that when you “add” to an infinite set, it’s so absurd that not even YOU are arguing that! ) so the only argument you think you have is removal!

This has been explained to you!

If you remove the first one:

Boy —>
Boy —> clone
Boy —> clone

Etc…

All that NEED fucking occur is that all the boys take ONE step forward, and EVERYONE is holding hands again. This is IMPOSSIBLE!! With finite sets!!

Impossible!!! It’s a fucking PROOF that the infinite works differently than the finite!!

You figured that out. That it disproved you.

So what did you do? You ignored it and then posted this:

Boy
Boy —> clone
Boy
Boy —> clone
Boy
Boy —> clone

Etc…

And I jumped in and said “if you move the first boy up one step and then the bottom two (now) up one step and the (now) bottom three up one step Etc… all at once, everyone will still be holding hands again! But only in infinity is this a FACT!! If this is finite, it’s impossible to do this! Thus: infinite and finite WORK differently!

And you know what ?

You blew me off!

That’s not what convergence is.

en.wikipedia.org/wiki/Convergent_series

This means that the infinite sum (0.9 + 0.09 + 0.009 + \cdots) converges to (1). (Which does not mean that it is equal to (1).)

It does mean that it’s a SUM!!!

YOU’RE the one who used the word “sum” incorrectly, not me!

But here you are AGAIN nit-picking over stupid shit and avoiding arguments that have to do with either:

1.) 0.999… 1 (or not)
2.) orders of infinity exist (or not)

Converges to means the same exact thing as “equals”

Magnus!! Who gives a fuck about this trivial shit anyways?!?!

You have arguments to look at!

I did not ignore it. I responded to it by stating that it’s not something that you can do because it is strictly forbidden by your previous claims.

Let’s go back to page 98 where I stated:

Note the bolded part.

In order to restore one-to-one correspondence between the two sets, there must be an unpaired clone to pair with an unpaired boy. But there is no such a clone. All of the clones are already paired. Thus, regardless of how you move your clones, you cannot restore one-to-one correspondence.

You responded to this by saying that the word “infinity” refers to a never-ending process of increase which means that new clones are added continually. So when we remove a clone, a new one is added automatically.

And my response to this was that the word “infinity” does not refer to a never-ending process of increase (that it does not refer to a process at all.)

That’s not true.

You’re still doing it! You’re ego is invested in nit-picking and not arguments!!!

There is a difference between ‘converges to’ (which is convergence) and ‘converges towards’ which is not convergence. But!! Even that’s a contradiction because the word convergence IN AND OF ITSELF is defined as the finite conclusion of a sequence or series. Infinite or not.

It’s part of your argument that infinite sequences are both finite and infinite sequences.

That in turn is part of your argument that infinite sequences are algorithms.

That in turn is part of your argument that the word “infinity” refers to a never-ending processes of increase.

That in turn is part of your argument that infinities do not come in sizes.

Not true.

This part is transitive:

1/9 implies 0.111…

0.111… implies 1/9

If they both imply each other, they are equalities.

I have no idea what that means.

And that’s why this debate is over. Because you don’t understand, really, much of anything said here!

But let me be kind to you for a moment!

2+3=5
3+2=5

That means 2 and 3 are transitive: they mean the same thing!

I’ve seen you write a bunch of fancy symbols, but you don’t even understand kindergarten math!

That’s why we are butting heads here!

This isn’t supposed to be a contest of beliefs but a cooperative effort to resolve disagreements. (But then again, this is a forum, so pretty much everything anyone does here is some sort of competition where people try to prove themselves to be the smartest guy in the room.)

What do you mean by “transitive”?

en.wikipedia.org/wiki/Transitive_relation

Either way, it’s definitely not true that (2) and (3) mean the same thing.

Magnus,

I have to admit, at this point, I enjoy teaching you because you don’t quit!

Transitive (strictly speaking) (as an example)

Is:

ab = ba

I gave you a more advanced version in the last post; what I should have said is that:

2+3 = 3+2

3+2 = 2+3

Etc…

When you introduce a new variable (such as “5”) (c) it becomes a different term than purely transitive, Wikipedia is wrong.

That looks like commutativity.

Here it is:
viewtopic.php?f=4&t=190558&p=2768316#p2768299

And you are ignoring it (: