Rational numbers == infinitely repeating sequences of digits

[untermensche]

And yet minutes ago you were finally coming around to the idea that strings represent numbers.

I have always said the string represents a value.

0.333 represents a unique value. 0.3333 represents a different value.

And because adding a digit changes the value I know 0.3333.... has no final value.

But there is a difference between 0.33 and 0.333

So the value is not 3 just because the digit is 3.

So you're saying the digit "3" refers to something other than the number 3?

The digit 3 alone represents nothing but itself. It is the symbol for an abstract representation of a certain value within an abstract conceptual scheme of values.

The digits 0.333 represent nothing but the value of the string as defined within a defined scheme of values. There is nothing else but a value.

So what about that Czech Tennis player? Does he become undefined when you can't type his name?

If his name is define as Ivan Lendlllllllll....

What is his name?

Can it be said?

 

[Jokodo]

I have always said the string represents a value.

Where you lying when you said that "There is nothing a string of 3's refers to but itself [i. e. the string of 3s]" in post 132 or have you changed your mind? It's gotta be one of the two unless you are just polluting the internet with randomly stringed together words bare of meaning then and now.

Where you lying when you said that "A digit is a number" in post 110 or have you changed your mind? It's gotta be one of the two unless you are just polluting the internet with randomly stringed together words bare of meaning then and now.

Where you lying when you said in post 89 that "[the digit 3] describes nothing else but itself" or have you changed your mind? It's gotta be one of the two unless you are just polluting the internet with randomly stringed together words bare of meaning then and now.

0.333 represents a unique value. 0.3333 represents a different value.

You're getting closer. 0.333 and 0.3333 signify different values. Not one value that's increasing with time.

In the same way 0.333... represents yet another unchanging and precisely defined value. No "final value" crap needed.

And because adding a digit changes the value I know 0.3333.... has no final value.

No, adding digits doesn't change the value of one and the same number, it creates a different label referring to a different number.
The number referred to by 0.333, for example, is exactly 333/1000, the number referred to by 0.3333 exactly 3333/10000. The number referred to by 0.3... is exactly 3/9 = 1/3.

So you're saying the digit "3" refers to something other than the number 3?

The digit 3 alone represents nothing but itself. It is the symbol for an abstract representation of a certain value within an abstract conceptual scheme of values.

The digits 0.333 represent nothing but the value of the string as defined within a defined scheme of values. There is nothing else but a value.

So what about that Czech Tennis player? Does he become undefined when you can't type his name?

If his name is define as Ivan Lendlllllllll....

What is his name?

Can it be said?

What if it can't? Does it make the person disappear? You're still way out there confusing labels and referents. Way out in "Australia is larger than Asia because it has four more letters" territory.

And, actually, "Jiří Hřebec" is a closer analogie closer. It's not a property of the number 0.333... itself that it can't be expressed in a finite string. It's an artifact from using a representational scheme that's poorly suited for that particular number. In base twelve, it comes out as 0.4 straight. Just like the ASCII character set isn't particularly well suited for Czech names.

 

[untermensche]

Where you lying when you said that "There is nothing a string of 3's refers to but itself [i. e. the string of 3s]"

The string has a value attached to it. An abstract value within an abstract system.

But the value of the string is just the value of the string.

It is no other thing.

You have made no criticism here.

Where you lying when you said that "A digit is a number"

A digit is a number. It has an abstract value attached to it.

Where you lying when you said in ... that "[the digit 3] describes nothing else but itself"

It is nothing but an abstract value.

It is nothing else.

What if it can't? Does it make the person disappear?...

It means the name can't possibly refer to a person since the person is here but the name can never be here.

 

[Jokodo]

The string has a value attached to it. An abstract value within an abstract system.

But the value of the string is just the value of the string.

It is no other thing.

You have made no criticism here.



A digit is a number. It has an abstract value attached to it.

Where you lying when you said in ... that "[the digit 3] describes nothing else but itself"

It is nothing but an abstract value.

It is nothing else.

What if it can't? Does it make the person disappear?...

It means the name can't possibly refer to a person since the person is here but the name can never be here.

So you're back to lying some more. A pity. For a moment I thought we were making baby steps towards basic intellectual honesty.

 

[untermensche]

You haven't demonstrated anything.

I would have no argument if I said 0.333 did not have a specific value. But it only has that value within a defined context.

But it has nothing else.

Remove it from that context and you are just transforming it, not giving us something it is referring to.

It is referring to it's value, to itself, and nothing else.

You have not demonstrated it is referring to anything else.

You have not demonstrated one thing.

 

[bilby]

The string has a value attached to it. An abstract value within an abstract system.

But the value of the string is just the value of the string.

It is no other thing.

You have made no criticism here.



A digit is a number. It has an abstract value attached to it.



It is nothing but an abstract value.

It is nothing else.



It means the name can't possibly refer to a person since the person is here but the name can never be here.

So you're back to lying some more. A pity. For a moment I thought we were making baby steps towards basic intellectual honesty.

Nah, he's just taking shuffling steps away from responding to this:

... I challenged you to find any instance of any mathematician anywhere who has used the phrase "final value" in the way you are using it here - to refer to a number.

Can you meet that challenge, or is this entirely your own stupidity?

bears repeating.

untermensche, can you meet that challenge?

 

[Jokodo]

The string has a value attached to it. An abstract value within an abstract system.

No, it doesn't have a value "attached to it". The value is entirely external to the string. The string "0.333..." represents the number 1/3 in decimal, but the number 1/5 in base 16 - and no number at all in bases 2 and 3 where "3" is not a valid digit.

But the value of the string is just the value of the string.

You may be talking about what the adults call "numbers" here.

It is no other thing.

You have made no criticism here.



A digit is a number.

Come on, are we really back to "1 + 3 = 13"?

It has an abstract value attached to it.

Where you lying when you said in ... that "[the digit 3] describes nothing else but itself"

It is nothing but an abstract value.

Which is not "itself", the digit "3". The digit "3" is a character containing to half-circles attached to each other at an angle in the center-right.

It is nothing else.

What if it can't? Does it make the person disappear?...

It means the name can't possibly refer to a person since the person is here but the name can never be here.

Does it make the person disappear?

 

[Jokodo]

You haven't demonstrated anything.

I would have no argument if I said 0.333 did not have a specific value. But it only has that value within a defined context.

But it has nothing else.

Remove it from that context and you are just transforming it, not giving us something it is referring to.

It is referring to it's value, to itself, and nothing else.

You have not demonstrated it is referring to anything else.

You have not demonstrated one thing.

I've demonstrated you're contradicting yourself. That leaves 4 possibilities:

1. You lied before.
2. You're lying now.
3. You have no clue what you're talking about, either then or now.
4. You've changed your mind.

I'm personally leaning towards 3, but I was giving you the benefit of doubt pretending for the sake of the argument it's 4. Be a good boy now and say "thank you" to the nice uncle!

 

[untermensche]

You've demonstrated no lies.

You claimed things were lies and one by one I showed you were nuts.

You have nothing.

You have given nothing to dispute that 0.3333 represents the value 0.3333 and NOTHING else.

You talk about imaginary lies because you have nothing.

How about addressing the issue here.

For once.

Prove to me that 0.3333 represents more than the value 0.3333 within a defined scheme.

Stop your hand waving bullshit!

You have not demonstrated anything. That you can't understand that shows you to fit #3 above.

 

[untermensche]

No, it doesn't have a value "attached to it". The value is entirely external to the string.

The value is expressed by the string.

The string "0.333..." represents the number 1/3 in decimal

All you can do is claim it. You can't prove anything.

It does not represent anything but itself.

What you have given me is an equation that produces the decimal. The decimal exists if we carry out the implied division within a predefined scheme. If you can't see that you are truly blind.

You have not proven they are the same thing.

A product and the equation that produces it are not the same thing.

That is nonsense!

Come on, are we really back to "1 + 3 = 13"?

Only in your twisted mind.

You have never demonstrated this nonsense with any argument. You have merely claimed it a few times after pulling it from thin air.

It is nothing but an abstract value.

Which is not "itself", the digit "3".

The digit has a context.

The value is all the digits in context.

But the digit has a specific value in the context.

It has nothing else.

0.4443444

The 3 has the value 0.0003 in this context.

It does not have anything else.

You have not demonstrated it has anything else.

It means the name can't possibly refer to a person since the person is here but the name can never be here.

Does it make the person disappear?

You have merely placed the person there directly from thin air. You have just assumed your conclusion. You have not proven the name and the person are the same thing.

But if the name can never be said and it is supposedly his name then that is really saying he has no name. No name that could possibly exist.

 

[Jokodo]

0.4443444

The 3 has the value 0.0003 in this context

See, that's what I'm talking about.

Earlier you claimed that 3 can only ever refer to 3. Now you're saying that 3 "in this context" refers to 0.0003. One of them has to be false. Did you lie then, are you lying now, have you changed your mind, or are you too stupid to understand the contradiction?

 

[untermensche]

0.4443444

The 3 has the value 0.0003 in this context

See, that's what I'm talking about.

Earlier you claimed that 3 can only ever refer to 3. Now you're saying that 3 "in this context" refers to 0.0003. One of them has to be false. Did you lie then, are you lying now, have you changed your mind, or are you too stupid to understand the contradiction?

3 can only refer to 3.

And 0.0003 can only refer to 0.0003. A decimal point and 0's creates a different value within a decimal system.

This is not hard.

How many times have I said the value is dependent on context?

But the value within the context is all there is. There is nothing else but an abstract value in an abstract context. And only something with training can see it.

There is NOTHING else.

You have not demonstrated there is something else. You have claimed it.

 

[Jokodo]

That you can't understand that shows you to fit #3 above.

... in which you use "3" to refer to something else than 3...

 

[untermensche]

That you can't understand that shows you to fit #3 above.

... in which you use "3" to refer to something else than 3...

What else besides itself does it point to? The sentence after it has a meaning unrelated to "3". Are you saying 3 also equals "You have no clue what you're talking about, either then or now." Show me your work and the equations you arrived at to conclude that sentence = 3.

You have this religious faith that the symbols for values taken in their predefined context point to something besides the value.

You have not demonstrated it once.

 

[Jokodo]

That you can't understand that shows you to fit #3 above.

... in which you use "3" to refer to something else than 3...

What else besides itself does it point to? The sentence after it has a meaning unrelated to "3". Are you saying 3 also equals "You have no clue what you're talking about, either then or now."

It doesn't eqal the sentence, it refers to it, in this context. The string is a fucking label, and I made it refer to the sentence when I typed the list. In other contexts, it tends to refer to a number, but it no more equals that number than it equals my sentence.

Show me your work and the equations you arrived at to conclude that sentence = 3.

I don't have to. Deep inside, you know it's true -- you just used it that way yourself.

- - - Updated - - -

You have this religious faith that the symbols for values taken in their predefined context point to something besides the value.

Symbols point to referents. We seem to agree about that though you have a weird way of saying it. But they are not their referents.

 

[untermensche]

What else besides itself does it point to? The sentence after it has a meaning unrelated to "3". Are you saying 3 also equals "You have no clue what you're talking about, either then or now."

It doesn't eqal the sentence, it refers to it, in this context.

In context it merely precedes the sentence. It is still only a symbol for an abstract value within an abstract value system.

Any sentence could have been placed next to it.

The string is a fucking label

A label for a specific value within a value scheme.

And NOTHING else.

Symbols point to referents.

The symbol is the referent. It refers to a value as defined in a value system.

 

[Jokodo]

In context it merely precedes the sentence. It is still only a symbol for an abstract value within an abstract value system.

Any sentence could have been placed next to it.

Indeed. It's called the "arbitrariness of the sign". You can google it.

The string is a fucking label

A label for a specific value within a value scheme.

And for another value in another scheme.

And NOTHING else.

You just used it to refer to something else.

Symbols point to referents.

The symbol is the referent.

...with which we're back to "1 + 3 = 13"

 

[Jokodo]

Come on, are we really back to "1 + 3 = 13"?

Only in your twisted mind.

You have never demonstrated this nonsense with any argument. You have merely claimed it a few times after pulling it from thin air.

I's a logical consequence of claiming that digits/numeric strings and the numbers (or if you prefer, "values") they refer to (or if you prefer, "represent") are the same thing. We know what we get from putting a digit "3" next to a digit "1" - if you don't believe it, you can cut them out of cardboard and shift them around on the floor. If numbers and digits are really the same thing, we can thereby infer that 1 + 3 = 13 (or maybe 31).

And have you found a mathematician talking about a number's "final value"?

 

[untermensche]

Indeed. It's called the "arbitrariness of the sign". You can google it.

I have no time for pointless fishing trips.

The string is a fucking label

A label for a specific value within a value scheme.

And for another value in another scheme.

Placing a value in one value scheme into another scheme is still saying the number has an abstract value in an abstract value system. And nothing more.

If you are transforming some digits into other digits because you have a new value system then a transformation is necessary.

A transformation is to change something. It is not saying it is the same thing as something.

You just used it to refer to something else.

I did not. I said the point came after it.

Symbols point to referents.

The symbol is the referent.

Meaning it refers to a value within a value system that also may have the symbol "+" defined as well.

...with which we're back to "1 + 3 = 13"

Yes we are back to your pointless and meaningless hand waving.

That is a non sequitur pulled from thin air not something you have demonstrated.

 

[Jokodo]

I have no time for pointless fishing trips.

A label for a specific value within a value scheme.

And for another value in another scheme.

Placing a value in one value scheme into another scheme is still saying the number has an abstract value in an abstract value system.

So you've dropped your claim that "a number is what is right before you. What you apprehend"? That's what saying it has an abstract value amounts to, you know?

And nothing more.

If you are transforming some digits into other digits because you have a new value system then a transformation is necessary.

A transformation is to change something. It is not saying it is the same thing as something.

The string "0.333..." is the same physical object when it is used to a number (if you insist: close to or) equal 1/5 in base-16 notation and when it refers to a number (close to or) equal 1/3 in base-10 notation. Yes or no?

The string "0.333" is the same physical object when it is used to refer to the number 333/1000 and when it is used to refer to the 333rd paragraph/example/theorem of the preface (chapter 0) of a poorly structured book. Yes or no?

Since 1/5 != 1/3, and a paragraph is not a rational number, it follows that representing a certain value is not an intrinsic property of the string, anymore than being represented by a particular string is an intrinsic property of that value.

Welcome to semiology 101. You just got to know the concept of a symbolic mapping.

You just used it to refer to something else.

I did not. I said the point came after it.

Symbols point to referents.

The symbol is the referent.

Meaning it refers to a value within a value system that also may have the symbol "+" defined as well.

...with which we're back to "1 + 3 = 13"

Yes we are back to your pointless and meaningless hand waving.

That is a non sequitur pulled from thin air not something you have demonstrated.

It's a logical consequence of your earlier claim that digits and the values they refer to are the same thing. Have you dropped that nonsensical claim yet?

And have you found a mathematician talking about a number's "final value"?