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.
Here’s a flowchart demonstrating a structured approach to discussing ideas, one that is conducive to resolving disagreements. (This is no quick fix, so no promises of the form “Make everyone agree within a record period of time!” are made. My sole claim is that it’s an approach that is better than other approaches. If it takes more than (1,000) pages for people to come to agreement using this approach, it merely means that other approaches would have taken much longer than that.)
Ecmandu loves algorithms, so he should be able to appreciate this flowchart: How to Discuss Ideas
It’s a pretty simple flowchart, actually.
So when I say that someone did not address a claim I made, I am simply saying that they did not follow the steps outlined in this algorithm.
The key part is the idea that the right way to respond to mere assertions is different from the right way to respond to arguments.
For example, if I make a statement that (0.9 \neq 1), without explaining how I arrived at such a conclusion, the adequate way to respond to it, in case you disagree with it, is by offering a counter-argument i.e. by providing an argument that proves that (0.9 = 1). For example:
Whether or not the argument is sound, whether or not its conclusion is true, whether or not the person understood the original claim and whether or not the person presenting such an argument is stupid or smart are completely irrelevant. The response is an adequate one for the simple reason that it provides a counter-argument to a previously made claim.
However, that wouldn’t be a proper response in the case I offered the following argument . . .
(1) is a number
(0.999\dotso) is not a number because it does not end
A number cannot be equal to something that is not a number
Therefore, (1) is not equal to (0.999\dotso)
Here, you have to show what’s WRONG with the presented argument and not merely argue against the conclusion. You have to explain why you think the argument is UNSOUND. Is it logically invalid? If so, why? Are there any premises that are false? If so, which ones and why?
But if all you do is COMPLAIN about how other people are not up to your expectations, then you will get nowhere. You will waste your time and even achieve the opposite of what you wanted to achieve in the first place.
Let’s say the full argument of that imaginary person of mine goes something like this:
(0.999\dotso) has no end
Numbers must have an end
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.
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.
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.
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?
Every single opinion of every single stupid person is false.
Magnus Anderson is a stupid person.
Magnus Anderson has an opinion that (0.9 \neq 1).
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.
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.