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.
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.
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.