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Mowk wrote:On one side of the equals is the representation of a single whole unit with nothing to it's left and nothing to it's right, on the other is a decimal expression of 9/10th divided by 9/10 infinitely, filling all possible digits with a non-zero number. Infinitely less than 1.
All the math you want to throw at the question as proof is irrelevant, smoke and mirrors... a distraction.
Silhouette wrote:I've already addressed this issue, but let me tie it specifically to what you're saying to spare you from claiming that others such as phyllo are not paying attention when they are.
When I speak of the difference between representations and quantities I am speaking of the difference between concrete and abstract, the signifier and the signified.
Something like "1" is the "concrete signifier" that represents an "abstract signified" known as quantity.
Putting a value in the units column is one way of representating the same quantity as putting a zero in the units column and 9s in infinitely many orders of magnitude less than a unit (everything after the decimal point).
Two different representations: same quantity.
Another example to perhaps clarify what I'm getting at here:
In hexadecimal, the digits 0-F extend the digits 0-9 in decimal. "10" in decimal is "A" in hexadecimal.
Now, if we were to "borrow" this A from hexadecimal, which means "10" in decimal, and put it into a decimal number like so: "0.A", there is a zero in the units column, and yet the quantity represented could also be represented as a decimal "1".
Two different representations: same quantity.
Getting caught up in the appearance of each representation being different is merely superficial. By itself it doesn't say anything about the quantity "in itself".
Do you understand this?
In the decimal system, the digits to the right of the decimal point represent fractions having a denominator which is a multiple of 10. The first digit is 1/10 fraction, the second is 1/(10x10), the third is 1/(10x10x10), etc.Mowk wrote:You are thinking in terms of percentages.
The range between 0 and 1 in a percentage system has divided all possible values between 0 and 1 into only 100 places. 99 percent of 1 is very close to one.
But 1 of 99 pieces of a whole is not 99% of the whole it represents, just 1 percent of 1 whole number. 1 divided by 99 represents just 1 piece of of the whole 1, divided into 99 parts.
1 part of 10 parts, is 10 percent of 1 whole. 10 parts of 100 parts is still 10 percent of 1 whole.....
Correction. I don't pay much attention to some posts and some posters.I do agree with Mowk that, on average, and within this thread at least, Phyllo is not paying attention. Ever since the creation of this topic, his mindset has been "I don't find this question interesting so I'm going to answer it any way I like no matter how stupid it is because . . . why not?" thereby automatically disqualifying himself as a serious interlocutor. It's only slightly better than what Biguous is doing here and elsewhere.
Magnus Anderson wrote:I do agree with Mowk that, on average, and within this thread at least, Phyllo is not paying attention. Ever since the creation of this topic, his mindset has been "I don't find this question interesting so I'm going to answer it any way I like no matter how stupid it is because . . . why not?" thereby automatically disqualifying himself as a serious interlocutor. It's only slightly better than what Biguous is doing here and elsewhere.
Magnus Anderson wrote:Can you give us an example of two different base-10 representations that represent one and the same number?
phyllo wrote:For example, you are unable to make up your mind about whether infinity is a number or not.
You wobble back and forth as it suits you. You don't have a consistent point of view and so you don't have a consistent argument.
You don't understand convergence and divergence. Yet you insist on using series representations. The result is more inconsistent arguments.
Then there are the posts where you accuse people who disagree with you, of being blind followers of convention. I have no interest in those kinds of personal and manipulative posts.
Magnus Anderson wrote:That's because convergence and divergence are completely irrelevant.
Silhouette wrote:Yes. \(1\) and \(0.\dot9\).
You get the concept using symbols across number bases, and in radians - so clearly you understand how the appearance of the numbers differing doesn't necessarily matter - they can still represent the exact same quantity.
Thanks for confirming.
\(0.\dot3\) and \(\frac1{3}\) are likewise just different representations of the same quantity. Both represent the division of exactly 1 by exactly 3 to get a third exactly.
There's no problem dividing 9 by 3 in exactly the same way as any rational number with however many decimals - so using the exact same division there's no problem dividing 10 by 3 to get exactly \(3.\dot3\)
Why is the result of division okay sometimes but not others? It's exactly the same concept and any methods or processes to successfully achieve it do so in exactly the same way to the same success.
As such the decimal representation of \(3.\dot3\) ONLY works precisely because the 3 is recurring, never ending, infinite, with an undefined number of repetitions. It's not a problem that the remainder is never 0 to terminate a finite (rational) decimal.
As with all irrational numbers, the remainder never being 0 is the only way in which they can be exactly correct - you just have to respect the involvement of the undefined nature of infinity and what it means. That's where this mysterious ambiguous "remainder" is, which you're looking for - it's in your lack of respect and understanding of infinity/the undefined. It sure as hell isn't anywhere in the realm of the defined!
Silhouette wrote:So if you say an essential thing to understanding the topic is irrelevant, you can imagine it's not an issue?
It's either intentional out of bad faith or unintentional from incompetence - I think a mixture: except I don't think you are explicitly trying to argue in bad faith, I think it's just the usual psychological protections that people usually fall foul to that are getting in your way of changing your mind. If you weren't merely trying to bolster your own (lack of) argument, and instead you tried to understand see the sense in the arguments of others - take a leaf out of Mowk's book for this one - then we could get somewhere, but I think the inability also plays a part against you here too.
You like to say these psychological analyses of you are also "irrelevant", but they really aren't - for the same reasons as above ^
phyllo wrote:So you still don't think that 9/10, 99/100, 999/1000, 9999/10000 is getting closer to 1?
No.Nope I don't think what you have written is getting anywhere.
9 divided by 10 = .9
99 divided by 100 = .9
999 divided by 1000 = .9
All of your representations are going no where, stuck to the fist digit. You aren't plotting different numbers. It isn't getting any closer to one or zero.
Okay, then you should have no problems relating it to other numbers.It's a number. Thought it's obvious.
phyllo wrote:Is infinity an odd or even number?
In mathematics, parity is the property of an integer's inclusion in one of two categories: even or odd. An integer is even if it is divisible by two and odd if it is not even.
A formal definition of an even number is that it is an integer of the form n = 2k, where k is an integer;[3] it can then be shown that an odd number is an integer of the form n = 2k + 1 (or alternately, 2k - 1). It is important to realize that the above definition of parity applies only to integer numbers, hence it cannot be applied to numbers like 1/2 or 4.201.
Both interesting and odd, since you are using it to count digits and elements in a series and since you defined it as (1+1+1+...)The standard notion of parity, as indicated by Wikipedia, applies only to integers -- and infinity is not an integer.
phyllo wrote:Both interesting and odd, since you are using it to count digits and elements in a series and since you defined it as (1+1+1+...)
The set of integers consists of zero (0), the positive natural numbers (1, 2, 3, ...), also called whole numbers or counting numbers,[2][3] and their additive inverses (the negative integers, i.e., −1, −2, −3, ...).
So what's the value of $$\frac{\infty}{2} $$
More inconsistent properties.What would it mean for an infinite quantity to be even or odd?
Why is that even important?
Given a number 'n' we have ways to calculate n/2 which is also a number. If infinity was a number we ought to be able to calculate infinity/2 and it ought to be a number.And you're asking exactly what?
"The value of an expression" generally means "An equivalent expression that is of one's interest". "The value of 4 + 4 is 8" means that "8" is equivalent to "4 + 4" and that "8" is the kind of expression that one needs at that point in time (which is usually a single number.)
So I suppose you're looking for an equivalent expression . . . but what kind of equivalent expression? There are many expressions that are equivalent to ∞2 e.g. ∞4+∞4
.
I don't know why I would do any sort of mapping when we don't even agree to the value of 99/100. If you think that it's .9 and I think think that it's .99 then we have a major problem that needs to be resolved before moving on.Mowk wrote:did you map the points to a line divided into ten and into one hundred and one thousand with reference to 1 and 0?
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