untermensche
Contributor
What does any of that have to do with a definition that some thing repeats infinitely?
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Features
Rational numbers == infinitely repeating sequences of digits
- Thread starter lpetrich
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Jokodo
Veteran Member
Go to the original post and read the first sentence again: "A feature of rational numbers is that their decimal representations always have infinitely repeating sequences of digits" (emphasis added).
The property of having an infinite sequence of "3"s is a property of the decimal representation of the number that is expressed as "1/3" in fractional notation, as "0.1" in base 3, as "0.4" in base 12, or, as the previous poster hints at, as "10" in base 1/3. It is not a property of the number.
Saying about the number in question that is has infinitely repeating digits "3" is like saying that the continent Australia has nine characters. Continents don't have character counts and numbers don't have digits, infinitely repeating or otherwise, they have, respectively, e.g. areas and average altitudes and longest diameters, or prime factors and multiples and reciprocals etc. The labels "Australia" and "0.333..." have properties of their own, including a character counts, but those are uninformative about the properties of the continent/number.
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Actually, 1/3 in base 1/3 would be 10, not 1.
untermensche
Contributor
Nothing has infinity as a property.
There is no such thing as an infinite completed sequence.
There may be some thing that repeats infinitely.
In other words it repeats without any possibility of ending.
bilby
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Like your erroneous responses to threads about infinities.
untermensche
Contributor
No.
Totally unlike anything a human can or will ever experience.
But your simple faith is something common.
Jokodo
Veteran Member
That's why it's impossible to ever fully write out the decimal representation of the number 1/3. It doesn't tell us anything interesting about the number, and it doesn't prevent us from even determining abstract properties the decimal representation would have, could it ever be fully written out.
untermensche
Contributor
It should tell you 0.333... has no final value.
1/3 is an approximation.
They are not the same thing.
But their difference is infinitely small so in the real world it makes no difference to say they are the same thing. Nothing will happen.
But in the real world it is impossible to break anything into exactly 1/3 and 2/3 of the original. The break is always an approximation.
1/3 does not exist in the real world.
Jokodo
Veteran Member
the number 0.333... or the string "0.333..."?
Thanks for the effort, but we already knew you were delusional (if anything, 0.333.. is an approximation; 1/3 is exact as exact can be).
Next question?
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untermensche
Contributor
It is an endless string of numbers.
I don't share your religious faith so you merely claiming it means nothing.
It is like a Christian talking about the soul.
Something only seen with faith.
The string that is defined to never ends can end if we have enough faith.
Jokodo
Veteran Member
Noone said so. The adults are talking about numbers. What you're doing is literally like confusing the continent Australia and the Word "Australia" and concluding it's almost twice as Big as Asia which only has 5 characters.
untermensche
Contributor
It's not adults talking about numbers.
It's the faithful saying they don't care the string of numbers can't possibly end.
We can just pretend it does.
I agree.
Pretending is possible.
A string that continues infinitely is not some mystical other thing. Although it is possible to pretend it is equivalent to some other thing. Pretending is a human possibility.
But it is a string that continues infinitely.
It's the faithful saying they don't care the string of numbers can't possibly end.
We can just pretend it does.
I agree.
Pretending is possible.
A string that continues infinitely is not some mystical other thing. Although it is possible to pretend it is equivalent to some other thing. Pretending is a human possibility.
But it is a string that continues infinitely.
Jokodo
Veteran Member
Exactly. And the steig "Australia" has 4 more characters than "Asia"
untermensche
Contributor
Are either defined to repeat infinitely?
Land masses exist without any human label.
Nothing in mathematics exists until some humans invents it.
Land masses exist without any human label.
Nothing in mathematics exists until some humans invents it.
Jokodo
Veteran Member
That may be so, but it's irrelevant to whether the label and what it refers to can be equated.
Also, landmasses may exist but continents most certainly don't independently of definitions
untermensche
Contributor
A value can be expressed infinite ways.
1 = 1/1
1 = 2/2
And so forth infinitely.
What exactly is the magic number that represents all those expressions?
1 = 1/1
1 = 2/2
And so forth infinitely.
What exactly is the magic number that represents all those expressions?
Jokodo
Veteran Member
Yes, entities can have multiple labels. How is this relevant? And isn't it contradicting what you said earlier, when you denied that 1/3 and 0.333... could be the same thing because the labels differ?
untermensche
Contributor
Equivalence does not mean "the same thing".
6 x 3 = 9 x 2
6 x 3 = 9 x 2
bilby
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Well, there you have it. Everyone is wrong, except the guy who is able to see that eighteen doesn't equal eighteen.
untermensche
Contributor
The point sailed way above your head.
You have nothing to add here.
As usual.
You have nothing to add here.
As usual.
Jokodo
Veteran Member
Equivalence of labels means they refer to the same thing. That's even true whether the thing exists out in the wild or is purely a human invention.
We can state that 0.3... and 1/3 and duodecimal 0.4 are the same number whether or not numbers exist prior to humans defining them, just as we can say that "Gandalf", "Mithrandir", "Tharkûn", "Olórin", "Incánus" are the same person without believing that Middle Earth is real. So your entire discussion about "but humans invented numbers" is off mark.