# Thread: Rational numbers == infinitely repeating sequences of digits

1. Dodge.

But at least you admit that the terms have all been defined.

None exist before they are defined.

And of course if something is defined as one thing it means it is not some other thing defined differently.

2. Originally Posted by untermensche
Dodge.

But at least you admit that the terms have all been defined.
They, the terms you use, lack any definition.

None exist before they are defined.
If that is so, all your claims are literally meaningless as long as you refuse to define your terms. Not even wrong, content-free. Thanks for admitting.

And of course if something is defined as one thing it means it is not some other thing defined differently.
Non-sequitur.

3. Pathetic.

0.33333.... does not refer to 1/3.

It does not refer to anything but itself.

1/3 is just an equation that creates 0.3333...

An equation that produces something is not referring to it.

You have a strange religion.

4. Originally Posted by untermensche
Pathetic.

0.33333.... does not refer to 1/3.
The truth value of that statement is undefined as long as you refuse to clarify what it is you wish to talk about.

It does not refer to anything but itself.
The truth value of that statement is undefined as long as you refuse to clarify what it is you wish to talk about.

1/3 is just an equation that creates 0.3333...
Hey, we're making progress: a statement that's clear enough to be determined false!

"A common fraction is a numeral which represents a rational number. That same number can also be represented as a decimal, a percent, or with a negative exponent. For example, 0.01, 1%, and 10−2 all equal the fraction 1/100. " - https://en.m.wikipedia.org/wiki/Fraction_(mathematics)

5. Originally Posted by Jokodo
The truth value of that statement is undefined as long as you refuse to clarify what it is you wish to talk about.
Worthless dodge. You don't want definitions.

When I tried to work towards a definition of "3" you wanted no part of it.

You started. We agreed it was a pattern.

That is as far as you would go towards defining it. I said it was a specific pattern and you changed the subject.

So all we have so far is "3" is a specific pattern.

If we can agree with this we can possibly move towards a definition.

But you really don't want a definition.

6. Originally Posted by untermensche
Originally Posted by Jokodo
The truth value of that statement is undefined as long as you refuse to clarify what it is you wish to talk about.
Worthless dodge. You don't want definitions.
It's not a dodge, it's a fact.

When I tried to work towards a definition of "3" you wanted no part of it.

You started. We agreed it was a pattern.

That is as far as you would go towards defining it. I said it was a specific pattern and you changed the subject.

So all we have so far is "3" is a specific pattern.
What "3"?

If we can agree with this we can possibly move towards a definition.
You're not going to get me to agree to a claim that cannot possibly have a truth value. Again, what "3"?

But you really don't want a definition.
I've been begging you to define your terms since forever.

7. Originally Posted by Jokodo
What "3"?

But you really don't want a definition.
I've been begging you to define your terms since forever.
I had given you a definition of "3" many times.

"3" is a symbol that can be assigned to a value, an abstract value, imaginary value, conceptual value, within a predefined system of values.

Once assigned within a system it is nothing else.

It does not point to any other system of values.

Once you have a system of values you can also create specific abstract operations that can be carried out on those values to produce different values.

So the value 1 and and the value 3 point to nothing but themselves within a specific value system.

But if you divide 1 by 3 (shorthand 1/3) you can create a new value that also only points to itself within the system of values.

8. What "3"?
The "3" I'm looking at is a pattern of differently illuminated pixels. Of course, this cannot what you're talking about since it makes almost everything that follows false.
But you really don't want a definition.
I've been begging you to define your terms since forever.
I had given you a definition of "3" many times.
Never one that's consistent with even half of your claims.

"3" is a symbol that can be assigned to a value, an abstract value, imaginary value, conceptual value, within a predefined system of values.
I think you want to say "can be used/interpreted as a symbol", but I'll let this pass.

Once assigned within a system it is nothing else.
Which "it"? The pattern of differently illuminated pixels or the symbol created by interpreting it as a symbol? Or the value it has been assigned? Your claim is clearly false of the first, which is still a pattern of differently illuminated pixels whatever else it may be.

It does not point to any other system of values.
What's that "it" again that's clearly not the "3" I'm looking at?
Once you have a system of values you can also create specific abstract operations that can be carried out on those values to produce different values.

So the value 1 and and the value 3 point to nothing but themselves within a specific value system.
So it's the values you want to talk about? Too bad for you this makes all of your talk about final values gibberish. Also, what would it even mean for an abstract value to point even at itself?

But if you divide 1 by 3 (shorthand 1/3) you can create a new value that also only points to itself within the system of values.
That doesn't follow even if I allow you to jump back between the word d-o-g, the species canis lupus familiaris, and my neighbors' terrier at will.

9. Originally Posted by Jokodo
The "3" I'm looking at is a pattern of differently illuminated pixels. Of course, this cannot what you're talking about since it makes almost everything that follows false.
How the pattern is generated is meaningless.

All that is required is you have a mind that can recognize it as a distinct pattern.

You clearly recognize the pattern since you can refer to the same pattern I do.

This is nothing but hand waving nonsense.

Never one that's consistent with even half of your claims.
You've shown no inconsistencies.

"3" is a symbol that can be assigned to a value, an abstract value, imaginary value, conceptual value, within a predefined system of values.
I think you want to say "can be used/interpreted as a symbol", but I'll let this pass.
No it is a symbol. It symbolizes a value within an imaginary value scheme. There is a one to one correspondence between a symbol and an imagined value. A symbol in context only has one value.

Once assigned within a system it is nothing else.
Which "it"? The pattern of differently illuminated pixels or the symbol created by interpreting it as a symbol? Or the value it has been assigned? Your claim is clearly false of the first, which is still a pattern of differently illuminated pixels whatever else it may be.
The pattern is merely what the mind recognizes. A symbol is a recognized pattern that can refer to some other thing. The symbol points to a specific value within a predefined scheme.

The "it" is the one to one correspondence between a specific symbol in context and it's value within a predefined scheme.

It does not point to any other system of values.
What's that "it" again that's clearly not the "3" I'm looking at?
If you see a "3" and know its value then you know it as is a specific value within a predefined value scheme.

You know it as nothing else.

But if you divide 1 by 3 (shorthand 1/3) you can create a new value that also only points to itself within the system of values.
That doesn't follow even if I allow you to jump back between the word d-o-g, the species canis lupus familiaris, and my neighbors' terrier at will.
Saying 1/3 is shorthand for 1 divided by 3 makes no sense to you?

10. Originally Posted by untermensche

How the pattern is generated is meaningless.

All that is required is you have a mind that can recognize it as a distinct pattern.

You clearly recognize the pattern since you can refer to the same pattern I do.

This is nothing but hand waving nonsense.

You've shown no inconsistencies.
Do I really have to dig out the post where you said "3" doesn't refer to anything but itself? Where you talking about a different than now when you say it refers to an abstract value?

"3" is a symbol that can be assigned to a value, an abstract value, imaginary value, conceptual value, within a predefined system of values.
I think you want to say "can be used/interpreted as a symbol", but I'll let this pass.
No it is a symbol. It symbolizes a value within an imaginary value scheme. There is a one to one correspondence between a symbol and an imagined value. A symbol in context only has one value.
If by "in context" you mean "as long as we interpret it that way", this is a tautology. Otherwise it's false. The string "3.0" can refer to an integer 3 (e.g., the length of an array) only we need to convert it to real to perform floating point arithmetic on it (e. g., take its mean); it can refer to an exact real value; it can be shorthand for 3.0+/-0.05 when talking imprecise measurements (in this case it's distinct from 3.00), or it can refer to theorem #0 of section #3.

Once assigned within a system it is nothing else.
Which "it"? The pattern of differently illuminated pixels or the symbol created by interpreting it as a symbol? Or the value it has been assigned? Your claim is clearly false of the first, which is still a pattern of differently illuminated pixels whatever else it may be.
The pattern is merely what the mind recognizes.
That may be so, but it doesn't make the pixels go away.
A symbol is a recognized pattern that can refer to some other thing. The symbol points to a specific value within a predefined scheme.

The "it" is the one to one correspondence between a specific symbol in context and it's value within a predefined scheme.
So, substituting your definition, we get: Once assigned within a system the one to one correspondence is nothing else. That's not a meaningful statement.

It does not point to any other system of values.
What's that "it" again that's clearly not the "3" I'm looking at?
If you see a "3" and know its value then you know it as is a specific value within a predefined value scheme.

You know it as nothing else.

But if you divide 1 by 3 (shorthand 1/3) you can create a new value that also only points to itself within the system of values.
That doesn't follow even if I allow you to jump back between the word d-o-g, the species canis lupus familiaris, and my neighbors' terrier at will.
Saying 1/3 is shorthand for 1 divided by 3 makes no sense to you?
Sure it does. It doesn't however make it so that the operation rather than the value it produces is the only thing it refers to and it certainly doesn't make it so that that value must and not shared by other representations, or as the result of other operations.

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