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Rational numbers == infinitely repeating sequences of digits
- Thread starter lpetrich
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untermensche
Contributor
You believe in magic. A magical world where numbers exist before humans invent them. A heaven for numbers.
To you the number is not really the number seen.
It is by some magic really something else.
Magical absurd thinking.
That is all you offer.
1 only equals 1 if we arbitrarily ignore all the ways they are different, like in a different place. It is a mental operation, a mental act of abstraction.
1 only equals 1 if a human arbitrarily wants it to, because there is utility in pretending it is so.
lpetrich
Contributor
Except that rational numbers can also have non-terminating continued fractions. A constant-coefficient CF has this expression for its value:
\( x = a + \frac{b}{x} \)
This gives a quadratic equation for x, and such an equation can have rational as well as irrational solutions. In general,
\(x = \frac12 \left( a \pm \sqrt{a^2 + 4b} \right) \)
For instance,
\( x = 3 + \frac{4}{x} \)
has solutions x = -1 and x = 4, both obviously rational numbers.
Jokodo
Veteran Member
Your right. I have used such an example when teaching "How not to solve a quadratic equation..."
untermensche
Contributor
This is your defense of your silly beliefs?
Some worthless claim of "dualism"?
You can't tell me what a body is or what a mind is.
No less tell me that believing in both is some problem.
Jokodo
Veteran Member
A problem it may not be, but magical thinking it is. That's why it's ironic you go around calling others out for magical thinking.
untermensche
Contributor
Your conclusion it is magical thinking is based entirely on ignorance.
You don't know what a body is or what a mind is.
But something that is defined to repeat without end is known by the definition. And the definition doesn't just disappear capriciously.
In definitional schemes, like mathematics, the definer makes all the rules up. And the rules since invented are rigid and unchanging.
Jokodo
Veteran Member
The rules don't say "numbers and strings are the same thing". If I ask my computer to tell me what is 3 * 3, it will give me a 9 (the number designated by the string "3" in decimal notation, taken 3 times, represented in decimal notation). If I ask it what is "3" * 3, it will give me "333" (the string "3" repeated 3 times); if i ask it what is "3" * "3", it gives me a TypeError.
untermensche
Contributor
That is something out of left field.
How computers make use of numbers is totally how humans program them. They could be programmed to do something else with those commands if that was desired.
But saying a string has no last digit actually means something.
Of course we can pretend the string ends and move from there and see what happens.
But we shouldn't forget about the pretending.
In calculus we can pretend a slice is 0. We can pretend nothing is something.
But we should not forget we are just pretending.
How computers make use of numbers is totally how humans program them. They could be programmed to do something else with those commands if that was desired.
But saying a string has no last digit actually means something.
Of course we can pretend the string ends and move from there and see what happens.
But we shouldn't forget about the pretending.
In calculus we can pretend a slice is 0. We can pretend nothing is something.
But we should not forget we are just pretending.
Jokodo
Veteran Member
Sure they could. But they aren't because that would be defying the definition. Who was it again that said two posts back that "n definitional schemes, like mathematics, the definer makes all the rules up."?
It means very little when talking about numbers.
untermensche
Contributor
If one capriciously decides it is so, yes.
But a number is what is right before you. What you apprehend.
It is not some magical equivalence in the ether of the mind.
repoman
Contributor
To be able to talk about this topic in an accurate manner, you really have to be at the top of technical proficiency. The way that terms are used in math theory is so crazily dense, yikes!
Now, there is a possibility that between the verbal semantics and the mathematical semantics that the could be a confusion between these terms.
Also, it is true that the math is what humans have made and not assured to be reality, but closer than an armchair bullshitter will give.
As an example, how do we know that higher spatial dimensions actually follow the rules that we have ascribed to them. Perhaps 8th dimensional beings are right now having a chuckle at our version of the 8th dimension. Yes, we have extrapolated how it should work, but maybe reality has a surprise for us. This is not to disparage the mathematicians who work on this, they are brilliant and super cool and probably they are right, but maybe not...
Now, there is a possibility that between the verbal semantics and the mathematical semantics that the could be a confusion between these terms.
Also, it is true that the math is what humans have made and not assured to be reality, but closer than an armchair bullshitter will give.
As an example, how do we know that higher spatial dimensions actually follow the rules that we have ascribed to them. Perhaps 8th dimensional beings are right now having a chuckle at our version of the 8th dimension. Yes, we have extrapolated how it should work, but maybe reality has a surprise for us. This is not to disparage the mathematicians who work on this, they are brilliant and super cool and probably they are right, but maybe not...
untermensche
Contributor
There is no confusion when something is specifically defined to go on without end.
You know, in the title of this thread.
"infinitely repeating sequences of digits"
Is something that repeats infinitely defined?
untermensche
Contributor
Yes it is. Except if one believes inFinitism. Something that you apparently do, untermensche.
I merely take definitions seriously once expressed.
"Repeating infinitely" means something.
It does not mean repeating for a while then stopping.
All rational people should believe in finitism.
Nobody has ever seen an infinity of any kind. That is not possible.
The belief in real infinities or completed infinities is irrational. It merely shows one does not take the definition seriously.
repoman
Contributor
ok, 1/3 IS 0.333...
what is wrong with you?
Are you just itching for a fight? Go to politics.
what is wrong with you?
Are you just itching for a fight? Go to politics.
Jokodo
Veteran Member
What's wrong with him is that he doesn't understand the difference between strings and numbers.
He literally thinks that 1/3 and 0.333... must be very different because one contains three letters and the other eight (and by definition is a placeholder for an infinite string).
untermensche
Contributor
If you choose to discount definitions and have faith they are the same thing they are.
That is allowed. Nothing stops that kind of thinking.
Kharakov
Quantum Hot Dog
I like 1/3 in base three. So easy. But we can make it easier. Base 1 third!
I think we should just make all numbers be specific bases. So 1/9th would be written in base 1/9th. And pi would be base pi. And 2/pi would be base 2/pi.
It makes things easier. All numbers are #1. They all win!
BTW, you owe me 1 dollar.