Is 1 = 0.999... ? Really?

[Ecmandu]

Magnus,

Stop projecting man! Fuck! Even I still do it from time to time! It’s annoying as fuck!

You (in stating) that 0.999... is not a number is saying the exact same thing I’m saying when I state that infinities are not objects.

We’re just using different terminology for the same conclusion.

If “all” doesn’t ever describe infinity, then infinity ceases to possibly be a noun, it forces it to be a verb.

[Magnus Anderson]

You (in stating) that 0.999... is not a number

That's not my statement.

[Ecmandu]

You (in stating) that 0.999... is not a number

That's not my statement.

Ok. You copied someone else’s statement. Prove that it’s wrong.

[Magnus Anderson]

I already did.

No possible being can hold “all” of an infinite sequence in their “minds eye” at once, all they can do is to infer it.

An object has an end. Say, a couch. Thus we call it a couch. Very simple. An infinite number of couches?

No way! We can infer it, but we cannot count it.

I don't see a syllogism here. I can't see it in a previous post either.

[Magnus Anderson]

Ok. You copied someone else’s statement. Prove that it’s wrong.

Alright.

Let's say the full argument of that imaginary person of mine goes something like this:

1) \(0.999\dotso\) has no end
2) Numbers must have an end
3) Therefore, \(0.999\dotso\) is a number

I disagree with the second premise. The word "end" is not defined with respect to numbers. What does it mean for a number to have an end or to have no end?

The first premise is stating that the infinite expression represented by \(0.9 + 0.09 + 0.009 + \cdots\) has no end. I agree with that. However, that infinite expression is a symbol, it is not the symbolized. It is that which represents, not that which is represented. It says NOTHING about that which is represented. So even if we accepted the second premise (that numbers must have an end), the conclusion does not follow.

[Ecmandu]

I already did.

No possible being can hold “all” of an infinite sequence in their “minds eye” at once, all they can do is to infer it.

An object has an end. Say, a couch. Thus we call it a couch. Very simple. An infinite number of couches?

No way! We can infer it, but we cannot count it.

I don't see a syllogism here. I can't see it in a previous post either.

Man you’re an asshole Magnus!

You have any idea how hard it is to write a syllogism?

You know what I’m saying, and you know what it means, and still you want a syllogism from ME!

Why don’t you write the fucking syllogism since in your other thread (in rant about the purpose of these boards) you criticized people for how lazy they are, and only non-lazy people are the only worthwhile beings - in other words walk that talk.

[Ecmandu]

Ok. You copied someone else’s statement. Prove that it’s wrong.

Alright.

Let's say the full argument of that imaginary person of mine goes something like this:

1) \(0.999\dotso\) has no end
2) Numbers must have an end
3) Therefore, \(0.999\dotso\) is a number

I disagree with the second premise. The word "end" is not defined with respect to numbers. What does it mean for a number to have an end or to have no end?

The first premise is stating that the infinite expression represented by \(0.9 + 0.09 + 0.009 + \cdots\) has no end. I agree with that. However, that infinite expression is a symbol, it is not the symbolized. It is that which represents, not that which is represented. It says NOTHING about that which is represented. So even if we accepted the second premise (that numbers must have an end), the conclusion does not follow.

Magnus!

You are so confused in this message!

Of course 0.999... is the symbol and not the symbolized. I’ve been saying that the whole fucking time!

The symbolized NEVER ends!!! NEVER is a temporal word!

[Magnus Anderson]

You know what I’m saying, and you know what it means, and still you want a syllogism from ME!

I don't understand the process of your reasoning which is why I am asking you to present a syllogism.

If it's too hard for you to write a syllogism, you have nothing to do on a philosophy forum.

Of course 0.999... is the symbol and not the symbolized. I’ve been saying that the whole fucking time!

The symbolized NEVER ends!!! NEVER is a temporal word!

My position is that it's the symbol, and not the symbolized, that never ends.

And when I say that it's the symbol that never ends, I do not mean to say that it's the symbol \(0.999...\) that does so. That symbol is a finite sequence of characters, so it does end. It's this other symbol that does not end -- the one that cannot fit inside a post (because posts are finite.) The "invisible" one, so to speak.

Let me try to explain this with a different number. Consider \(1.000\dotso\). This is a finite symbol because it is a finite sequence of characters. It represents \(1\). I am pretty sure you agree. This symbol, however, is a shorter version of another symbol -- the infinite one -- that also represents \(1\) despite the fact that it is infinite. It's a symbol best captured by the sentence "A one, followed by a dot, followed by an infinite number of zeroes". That thing is a symbol, it's not the symbolized. The symbolized is a number -- specifically, it is number \(1\) -- and numbers have no notion of end.

What does it mean to say that a number has an end or that it does not have an end?

[Ecmandu]

Magnus,

Syllogism wise, you’re asking me to prove something no human has ever proven before... it’s very HARD!! It could take years!

My sentences on the other hand are not HARD!

Think about what you’re asking first before you call me “lazy”

Magnus! Honestly dude!

“My position is that it’s the symbol and not the symbolized that never ends”

Wtf dude! That makes no mathematical sense to ANY mathematician!!!

Are you just saying shit to say shit?

Your deepest question though was about “what does it mean to say a number has an end or not an end”

That’s the hardest question in the world to answer!

Let me sleep on it!

[Magnus Anderson]

One more thing.

This is an acceptable response:

1) Every single opinion of every single stupid person is false.
2) Magnus Anderson is a stupid person.
3) Magnus Anderson has an opinion that \(0.9 \neq 1\).
4) Therefore, \(0.\dot9 \neq 1\) is false.

This is acceptable because it addresses the question posed in the OP which is "Is \(0.\dot9 = 1\)?"

This is an unacceptable response:

"The reason Magnus Anderson is wrong on this subject is because he can't accept the possibility that he is wrong because that would shatter his excessively positive perception of himself. He thinks he's smarter than everyone else, and his entire existence depends so much on this belief, that he simply cannot allow anything to disturb it. If he wasn't so arrogant, he'd have learned by now that \(0.\dot9 = 1\)."

This is unacceptable because it's an answer to an unrelated question that is "Why is Magnus Anderson wrong on this subject?"

It's quite simply off-topic.

To make it worse, the question assumes the correct answer to the question posed in the OP.

[Ecmandu]

One more thing.

This is an acceptable response:

1) Every single opinion of every single stupid person is false.
2) Magnus Anderson is a stupid person.
3) Magnus Anderson has an opinion that \(0.9 \neq 1\).
4) Therefore, \(0.\dot9 \neq 1\) is false.

This is acceptable because it addresses the question posed in the OP which is "Is \(0.\dot9 = 1\)?"

This is an unacceptable response:

"The reason Magnus Anderson is wrong on this subject is because he can't accept the possibility that he is wrong because that would shatter his excessively positive perception of himself. He thinks he's smarter than everyone else, and his entire existence depends so much on this belief, that he simply cannot allow anything to disturb it. If he wasn't so arrogant, he'd have learned by now that \(0.\dot9 = 1\)."

This is unacceptable because it's an answer to an unrelated question that is "Why is Magnus Anderson wrong on this subject?"

It's quite simply off-topic.

To make it worse, the question assumes the correct answer to the question posed in the OP.

Magnus, you’re too ignorant about the topic to know what you’re asking!

These are the HARDEST tasks in number theory!

[Magnus Anderson]

Think about what you’re asking first before you call me “lazy”

Noone called you lazy.

Syllogism wise, you’re asking me to prove something no human has ever proven before... it’s very HARD!! It could take years!

My sentences on the other hand are not HARD!

The purpose of this thread is to present and examine arguments, not to merely exchange beliefs.

“My position is that it’s the symbol and not the symbolized that never ends”

Wtf dude! That makes no mathematical sense to ANY mathematician!!!

Are you just saying shit to say shit?

That must be the case.

[Ecmandu]

Sorry for the tone... I get really cranky when my allergies act up and my body is filled with histamines.

[Ecmandu]

Magnus,

Basically you asked “what does it mean that a number has an end or not an end?”

That’s the hardest question in all of number theory.

There are two reasons why.

1.) Data doesn’t get destroyed in an ultimate sense... it can always be reconstructed. Thus all numbers are technically infinite

2.) every ‘finite’ number equals an infinity.

Much like my example of the number 1.

1=

1/2+1/2
1/4+1/4+1/4+1/4
1/8+1/8+1/8+1/8+1/8+1/8+1/8+1/8

Etc... you get the picture.

So your initial question here is not a bad question, it’s just not easy to answer!

[Magnus Anderson]

What's up, Ec?

I have a question for you. Are you willing to answer it?

What's the number of numbers that we can get by dividing \(1\) by a natural?

The number of such numbers is infinite, correct?

\(\frac{1}{1}, \frac{1}{2}, \frac{1}{3}, \dotso\)

Is there are a number greater than every number in that list?

There is, right? For example, \(2\) is greater than every single number in that list.

In fact, there are many such numbers: \(2\), \(3\), \(4\) and so on.

So if we can speak of numbers greater than every number of the form \(\frac{1}{n}\) where \(n\) is a natural number, why can't we speak of numbers greater than every integer?

I say "numbers" instead of "a number" intentionally.

[Ecmandu]

What's up, Ec?

I have a question for you. Are you willing to answer it?

What's the number of numbers that we can get by dividing \(1\) by a natural?

The number of such numbers is infinite, correct?

\(\frac{1}{1}, \frac{1}{2}, \frac{1}{3}, \dotso\)

Is there are a number greater than every number in that list?

There is, right? For example, \(2\) is greater than every single number in that list.

In fact, there are many such numbers: \(2\), \(3\), \(4\) and so on.

So if we can speak of numbers greater than every number of the form \(\frac{1}{n}\) where \(n\) is a natural number, why can't we speak of numbers greater than every integer?

I say "numbers" instead of "a number" intentionally.

Not that list, no. There are very complicated non-rational concepts that presumably defy lists.

Chaitin is famous (called chaitin numbers) for proving that an infinite list can only be expressed as a number enumerating it as itself.

[Iamthegodoftruth]

A does not equal not-A. Except when it does, but then you’ll have to call it something else. Since “A” is already taken.

[Ecmandu]

A does not equal not-A. Except when it does, but then you’ll have to call it something else. Since “A” is already taken.

This is moronic. There has never been an “A” that has ever equaled another “A”, if you think, subatomic particles. But because of our lack of perceptual acuity, they look exactly the same. All equality is, is a lack of perceptual acuity... we have something called ‘categories’ and we rely on them every second of everyday. These are platonic forms.

[felix dakat]

In the universe of more of less the model that gets the job done wins.

[Certainly real]

When I was reading through this, I noticed the following that seems to bring it all to a salient conclusion.

0.999... is not a quantity or fixed value. It is an endless series of diminishing decimal values. The ellipsis "..." means "infinitely" - "never ending". The decimals begin but never end - open ended. The fraction is never satisfied by the series.

1 is an obvious quantity and fixed value with a beginning and an obvious end.

the only alteration required is the acknowledgement that infinitely diminishing decimal series are technically not numbers or quantities. Such can be merely stated in a foot note. Nothing very serious changes anywhere.

It makes sense that "0.999..." is just an expression signifying that some ratio cant be expressed by a fixed number of digits (unlike 1). It isn't actually a number. And neither are all of those other expressions that end with "...". And apparently that is why the Wikipedia proofs are misleading.

To me, that seems like a "game over".

1 cannot equal 0.999...
1 = 1 and 0.999... = 0.999...

Compare the following:
1) That room is 9m long
2) That room is 9.999...m long
3) That room is 999...m long
4) That room is 999...cm long
5) That room is infinitely long

9m encompasses the measure 8.999...m and everything less than it. 9.999...m is a measure just as 8.999...m is a measure. 3 and 4 are identical in size because once infinity enters the equation, it makes no difference if the measuring unit is m or cm. 3, 4, and 5, amount to the same thing, though expressed differently. If we say 6) that room is 222...m long or 7) 111...km long, again we are saying 5 just with different symbols that would be relevant or significant in a finite context. Not in this context.

That there is one Existence, cannot be denied. That It is Infinite cannot be denied. That It accommodates (makes hypothetically possible) things within it that can have a beginning but no end, cannot be denied. Call such endless things with beginnings x. Call Existence E. Clearly, E and x are different. All xs are encompassed/sustained/made possible by E. As in the set of all xs is E. There's only one E, but there can be an endless number of xs. xs cannot be independent of E. E cannot be independent of E, therefore, E is truly independent/self-sufficient and self-containing/encompassing. E is truly/completely Infinite. No other thing is truly/completely Infinite. No other thing is complete Infinity.

[Ecmandu]

CR:

In strange loops: x is e.

Look up this concept. It’s very well known.

Also:

Look up holograms, also very well known.

[Certainly real]

I think it's interesting to note the following:

9.999... is bigger than 8.999... but 8.999... is the same size as 8.111...

It's as if the Infinitesimal/Infinite is what connects/separates 8 to/from 9 with 8.111... and 8.999... and all other 8.123... highlighting that connection.

Is this not more reason to think that Existence is in us and we are in It?

[Ecmandu]

I think it's interesting to note the following:

9.999... is bigger than 8.999... but 8.999... is the same size as 8.111...

It's as if the infinitesimal is what connects 8 to 9 with 8.111... and 8.999... and all other 8.123... highlighting that connection.

Is this not more reason to think that Existence is in us and we are in It?

You’re talking about a lot of different things here that you didn’t clarify.

Is the number 1 infinite?

Well... you think it’s greater than all infinitesimals combined.

Well...What then about the number 2?

It’s twice as great as all infinitesimals combined.

But if we’re talking about infinity, it’s a concept of endless, which means that infinitesimals are greater than 1... all of them!

But you say 1 is the greatest (the supreme)

[Ecmandu]

I think it's interesting to note the following:

9.999... is bigger than 8.999... but 8.999... is the same size as 8.111...

It's as if the infinitesimal is what connects 8 to 9 with 8.111... and 8.999... and all other 8.123... highlighting that connection.

Is this not more reason to think that Existence is in us and we are in It?

You’re talking about a lot of different things here that you didn’t clarify.

Is the number 1 infinite?

Well... you think it’s greater than all infinitesimals combined.

Well...What then about the number 2?

It’s twice as great as all infinitesimals combined.

But if we’re talking about infinity, it’s a concept of endless, which means that infinitesimals are greater than 1... all of them!

But you say 1 is the greatest (the supreme)

Let me put it this way...

If you added all the infinitesimals together, they’d all add up to less than infinity... that’s a contradiction because they ARE infinite!

[Certainly real]

Is the number 1 infinite?

No

Well... you think it’s greater than all infinitesimals combined.

I don't

Well...What then about the number 2?

It's a finite number like the number 1, 5, or 48934892480

It’s twice as great as all infinitesimals combined.

There is no 'all infinitesimals'. There is the Infinite and the Infinitesimal. They are both One and the Same. There is only One of It.

But if we’re talking about infinity, it’s a concept of endless, which means that infinitesimals are greater than 1... all of them!

1 is finite, so is 2, so is every other finite number. This is distinct from that which is truly Infinite (E), which both sustains/encompasses and separates all xs and finites from each other.