Is 1 = 0.999... ? Really?

What does it mean to say that (0.111\dotso) implies (\frac{1}{9})?

What I’m saying is that it’s true on the surface, but totally false!

Let me give you the example of why I was sent to hell, and then hell beyond hell:

My argument was simple:

If you make suicide and homicide as easy as you could possibly make it (set suicidal and homicidal tension to zero), that whatever survived, would have inherent purpose to live! That’s the solution to ethics!

The argument was flawless!

I was wrong!

The problem on a higher plane of existence with this argument is that you can’t destroy existence, this “flawless” argument only sends people to hell.

Your argument from your mind seems flawless to you, but it is false!

So you’re saying that the statement (“Infinite sequences are infinite sequences”) is false and that it only appears to be true?

And you’re also saying that some infinite sequences are finite and some are infinite?

Is that correct?

Magnus! I like you because you stick with it!

Obviously tautologies aren’t false: “infinite sequences are infinite sequences”

With math, as with MANY aspects of life, it isn’t that simple!

Here’s an infinite sequence:

0.333…

ALSO a NUMBER!!!

ALSO 1/3rd!!!

Multiple equalities are true for EVERY possible number!! That’s the way it works.

No! I’m saying EVERY possible number is represented by a finite and/or infinite sequence and the reverse!

It’s really not hard to prove that magnus!

That’s not an infinite sequence.

If infinite sequences are not infinite sequences then what kind of sequences are they?

Are they sequences that are both finite and infinite?

0.333… right?

Well it’s not an infinite SUM! 0.333… is a discernible pattern that goes on forever (thus an infinite sequence!)

This is the problem we’ve been having. Your second quote encapsulates this problem! “If infinite sequences are not infinite sequences, then what kind of sequences are they?”

Well… tautologically, an infinite sequence is an infinite sequence! No argument from me there!

They are ALSO finite! In the form of a simple step procedure (a finite algorithm). Every infinite sequence is equal to a finite algorithm; they are equal.

That’s all my point was.

Let me try to explain why (0.333\dotso) is not an infinite sequence.

When we ask “Is (0.333\dotso) an infinite sequence?” what we’re asking is “Does the symbol (0.333\dotso) represent an infinite sequence?”

This means that we’re asking what the symbol (0.333\dotso) represents and NOT what the symbol (0.333\dotso) is in itself.

When we ask “Are numbers sequences?” what we’re asking is “Does the word represent a sequence?”

Since the word “number” does not represent itself, we do not care about the fact that the word “number” is a finite sequence of letters. In other words, the fact that the word “number” is a finite sequence of letters does not mean that what the word “number” represents (= symbolizes = signifies) is a finite sequence of letters (or a sequence at all.)

In the same exact way, the fact that the symbol (0.333\dotso) is a finite sequence of characters does not mean that it represents a finite sequence of characters (or a sequence at all.)

That symbol, on its own, is a sequence consisting of (8) characters. But the symbol itself does not represent a sequence of (8) characters.

(0.333\dotso) is a symbol representing certain number. And it’s not the only symbol that represents that number. There are many other symbols representing the same number. There are finite sequences of characters such as (0.3 + 0.03 + 0.003 + \cdots) as well as infinite sequences of characters that we cannot write down (since they are infinite) but that we can represent using other symbols (e.g. what is represented by the statement “a sequence that starts with (0) followed by (.) and an infinite sequence of (3)'s” is an example of such a symbol.)

Anything can be represented using any kind of symbol. The fact that you can represent a number using an infinite sequence DOES NOT MEAN that that number is an infinite sequence.

You can represent numbers with horses. That does not mean that numbers are horses.

The symbol is not the symbolized.

Sure… the map is not the territory.

We also have a property called “inferential logic”. We know that “x” implies “y”.

We also have inferential proofs.

The most basic inferential proof (and this always happens with any infinity). Is:

1,2,3,4,5,6,7,8,9,10,11,12 etc…

We know inferentially that’s no number repeats and it always grows in size.

Can any being hold all those numbers in its head to prove it ? NO! That’s why it’s called an inferential proof!

We infer from the sequence!

This type of proof is used in all infinity math!

What makes it? A sequence, a set of instructions, a discernible pattern!

Yes! 0.333… is a discernible pattern. That’s all a sequence is or need be

What does that mean?
(I asked this question before, you ignored it.)

I probably didn’t answer it because I was so incredulous that you don’t know what it means!!

It means what it says!!!

For example:

Can you hold every (implied) digit of 0.999… in your head at once?

Of course you can’t! Nobody can!

What does it mean to say that someone can hold something in their head?

Does it mean that someone’s head is big enough for that thing to fit inside?

In other words, does it mean that the volume of one’s brain is equal to or greater than the volume of that thing?

If this is the case, what’s the volume of the infinite sequence that is ((1, 2, 3, \dotso))?

If the volume of every number in that sequence is exactly one infinitesimal (cm^3), then the total volume of that sequence (assuming that only its elements have volume) is exactly (1cm^3) (since infinity times infinitesimal is (1)) which makes the volume of that infinite sequence smaller than every human brain.

You were asked to clarify, not to repeat what you said.

That’s what communication is about.

On the other hand, the fact that something is larger than one’s head does not mean that it is a process. There are many things that are larger than our heads e.g. airplanes. Does not mean that airplanes are processes.

I like that analogy!

You can hold a plane in your “minds eye”, you cannot hold 0.999… in your “minds eye”

Does that help?

These are very abstract metaphors here!

In order to be able to see or visualize anything, one needs time. If you’re sitting in front of a TV and I’m flashing a picture on it (let’s say the picture is shown for no longer than (1) millisecond), you wouldn’t be able to tell me anything about it. The more you want to see or visualize something, the more time you need. If it takes you one second to visualize a single apple, it will take you an infinite number of seconds to visualize an infinite number of apples. If it takes you one infinitesimal second to visualize a single apple, it will take you a second to visualize an infinite number of apples.

Most importantly, the fact that we can’t see or visualize something within a finite period of time does not mean that that thing is a process.

Ahh… that’s an interesting argument. You gave me something new to work with.

If infinity is not a process(as I say it is), then the odds of an infinitesimal (say us in an infinite universe) are exactly zero percent! Actually, and I say this to the best mathematicians on earth (and hopefully you can understand it magnus!) if there are always infinitely larger infinities, and our cosmos is finite (or a lesser order of the highest infinity), than at the highest cardinality, there is a zero percent chance for our entire universe to exist!

If however, hyperreals can’t exist, then our odds of existing are not zero percent, but rather 100%.

I figured out a way to put this in layman’s terms…

Let’s say that only one penny exists in all of existence, but you have an infinite number of dimes (they never stop) - your odds of finding the penny are zero percent! As if it didn’t and never did exist.

I’d say the probability of finding a penny is (\frac{1}{\infty + 1}). That’s close to (0) but it’s not (0).

The question I want to ask is:

How does this prove that the word “infinity” refers to a process?

That’s a good question!

We have inferential proof.

We can inferentially prove the sequence 1,2,3,4,5,6,7. Etc… not only goes on forever (without repeat), but always increases in size.

We can’t actually “see” in our “minds eye” ALL of it!!

ALL is not a “word that infinity understands”. These are metaphors to be sure!

All assumes completion, such as the number 1, it’s abstracted as an “object” (again, a type of metaphor)…

But! Is infinity (or an infinite sequence) an object like the number 1 is?

The answer is a resounding “no”. Because it’s not an object, it’s a verb, it’s action itself.

What is inferential proof?

I can agree that the sequence ((1, 2, 3, \dotso)) has no end and that it contains no repetitions. However, I cannot agree that it increases in size.

Can you provide a syllogism?

If you cannot expose your reasoning, all we can do is tackle your claims by providing counter-arguments i.e. arguments that prove the opposite of what you say.

This means that, unless you expose your reasoning, all I can do is say that the term “infinite sequence” does not refer to something that exists in time which means that it cannot increase in size and that it’s not a process in the first place. I can back this up by quoting Wikipedia. But I’ve already done most of the work, so the only thing that is left right now is to ask you to expose your reasoning. Such a feat requires a degree of self-consciousness and I’m not really sure you can pull it off but one can always hope.