Rational numbers == infinitely repeating sequences of digits

[untermensche]

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?

The symbol in itself points to nothing.

Within a predefined scheme it represent an abstract value.

This means 3 pounds of wheat is not the same thing as walking 3 miles. The value is abstract. It can apply to many things.

The number points to an abstract value within a specific scheme.

Which means if I weigh some thing within one scheme I will get certain digits but within a different scheme I will get different digits.

The digits are confined to a specific scheme.

That another scheme produces different digits is meaningless. Those digits are still confined to one scheme. They only have one meaning within the scheme.

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?

It's not an object.

It is the result of dividing 1 by 3, or in other form 1/3.

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?

Answered above.

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?

You have included an operation.

The values are subject to the rules of the operation.

 

[Jokodo]

Do you also go around saying that "a dog is a monosyllabic furry mammal with typically four legs and a voiced stop consonant in the syllable onset", or that "Gandalf is a bisyllabic wizard from the Middle-Earth universe with a consonant cluster in the coda of the second syllable who is typically depicted with a long white beard"? The way you're equivocating labels and their referents here, and jumping back and forth between them in one and the same argument, these sound like things you might say.

If, on the other hand, these sound absurd to you, you might get a first idea of how absurd your ramblings are to people
over 8 years of age who got numbers when they came up in school.

 

[untermensche]

Do you also go around saying that "a dog is a monosyllabic furry mammal with typically four legs and a voiced stop consonant in the syllable onset", or that "Gandalf is a bisyllabic wizard from the Middle-Earth universe with a consonant cluster in the coda of the second syllable who is typically depicted with a long white beard"? The way you're equivocating labels and their referents here, and jumping back and forth between them in one and the same argument, these sound like things you might say.

Another tangential journey because you have no direct arguments.

You just place things out there and because they have labels you think you have made a point.

3 is a symbol

Within a predefined scheme it has a defined abstract value. It has nothing else within that scheme.

0.333 is 5 symbols.

Within a predefined scheme it has a defined abstract value. It has nothing else within that scheme. It is nothing else within that scheme. It is not pointing to anything else within that scheme.

 

[Jokodo]

The symbol in itself points to nothing.

Arbitrariness of the sign. You think you invented this stuff? It's not up to debate.

Within a predefined scheme it represent an abstract value.

This means 3 pounds of wheat is not the same thing as walking 3 miles. The value is abstract. It can apply to many things.

The number points to an abstract value within a specific scheme.

Which means if I weigh some thing within one scheme I will get certain digits but within a different scheme I will get different digits.

No. If you weigh some thing in one scheme, you'll get a certain number which can be expressed in various notations, including digit-based ones. You're missing at least one level of abstraction here. The 3 in "3 kilograms of wheat" is the same 3 as the one in "3 pounds of wheat" despite referring to different masses - and remains the same if you express it with the English word "three", with the decimal representation "3.0", or in binary as "11".

The digits are confined to a specific scheme.

They're clearly not. the binary string "11" ("three") uses the exact same configuration of digits as the decimal string "11" ("eleven").

That another scheme produces different digits is meaningless. Those digits are still confined to one scheme. They only have one meaning within the scheme.

Well, yes, sort of, to the last sentence - ambiguous schemes are pretty useless and therefore not widely employed. But that is again not a property of the strings, it's a property of the schemes.

It's not an object.

It is the result of dividing 1 by 3, or in other form 1/3.

Not according to you: "1/3 is really a rule not a value." or: "But 1/3 is not the same thing as 0.3333......"
Lying then, lying now, change of mind, or just confused?

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?

Answered above.

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?

You have included an operation.

The values are subject to the rules of the operation.

Not if the only thing the digit refers to is the digit, then the only applicable operation is concatenation.

The thing about the symbol '+' that's it's ambiguous in many schemes: It can refer to two different operations, concatenation and addition. Concatenation is undefined for numbers, addition is undefined for strings. The very fact that you even can interpret it as addition shows that part of you knows that numbers and digits are in fact two kinds of animals.

 

[Jokodo]

Do you also go around saying that "a dog is a monosyllabic furry mammal with typically four legs and a voiced stop consonant in the syllable onset", or that "Gandalf is a bisyllabic wizard from the Middle-Earth universe with a consonant cluster in the coda of the second syllable who is typically depicted with a long white beard"? The way you're equivocating labels and their referents here, and jumping back and forth between them in one and the same argument, these sound like things you might say.

Another tangential journey because you have no direct arguments.

You just place things out there and because they have labels you think you have made a point.

So special pleading it is. You recognise that saying "a dog is a monosyllabic furry English mammal with four legs and a voiced plosive in the onset" is absurd because it confuses the word "dog" with the animal dog, but then turn around and say things about numbers that only (barely) make sense when said of strings.

A "number that doesn't end" makes every bit as much sense as a "mammal of the English language" or a "four-legged word".

And if you're thinking they're gibberish, you're right.

 

[untermensche]

Arbitrariness of the sign. You think you invented this stuff? It's not up to debate.

This is not a point. It is an empty claim devoid if any argument. Meaningless.

No. If you weigh some thing in one scheme, you'll get a certain number which can be expressed in various notations

No. You are limited by a scheme to weigh something. You can only weigh something within a scheme.

And the weight is limited to the scheme. It has no other meaning but a value within a specific scheme.

The 3 in "3 kilograms of wheat" is the same 3 as the one in "3 pounds of wheat"

In the real world there is no such thing as exactly 3 kilograms of anything or exactly 1/3 of anything. In the real world there is no 0.3333.....

But the 3 only has meaning if it exists within a predefined scheme. It only is explained as part of a specific scheme.

despite referring to different masses

It refers to only one mass within it's defined scheme. The mass of 3 grams of coffee is the same mass as 3 grams of sugar.

- and remains the same if you express it with the English word "three", with the decimal representation "3.0", or in binary as "11".

Within each defined scheme, and a different base is a differently defined scheme, the numerical representation of the mass is unique to that scheme. The numerical representation, the string of digits, only has meaning within that scheme. If you change the scheme you will get a different string of digits but they only have meaning within that scheme. They do not mean more than a value within one scheme.

The digits are confined to a specific scheme.

They're clearly not. the binary string "11" ("three") uses the exact same configuration of digits as the decimal string "11" ("eleven").

The digit is a representation of a value within the scheme. That string "11" has a different value depending on the scheme it is defined within.

You have no point here.

Not according to you: "1/3 is really a rule not a value."

It is a rule saying to divide 1 by 3. That is all 0.33333... is. The product of carrying out the rule. It is not the same thing.

You have included an operation.

The values are subject to the rules of the operation.

Not if the only thing the digit refers to is the digit, then the only applicable operation is concatenation.

The digit in context refers to an abstract value. Nothing more.

You have shown no magical thing behind these digits.

They refer to an abstract value within an abstractly defined scheme. Nothing more.

 

[Jokodo]

Theyis not a point. It is an empty claim devoid if any argument. Meaningless.



No. You are limited by a scheme to weigh something. You can only weigh something within a scheme.

And the weight is limited to the scheme. It has no other meaning but a value within a specific scheme.

The 3 in "3 kilograms of wheat" is the same 3 as the one in "3 pounds of wheat"

In the real world there is no such thing as exactly 3 kilograms of anything or exactly 1/3 of anything. In the real world there is no 0.3333.....

But the 3 only has meaning if it exists within a predefined scheme. It only is explained as part of a specific scheme.

despite referring to different masses

It refers to only one mass within it's defined scheme. The mass of 3 grams of coffee is the same mass as 3 grams of sugar.

- and remains the same if you express it with the English word "three", with the decimal representation "3.0", or in binary as "11".

Within each defined scheme, and a different base is a differently defined scheme, the numerical representation of the mass is unique to that scheme. The numerical representation, the string of digits, only has meaning within that scheme. If you change the scheme you will get a different string of digits but they only have meaning within that scheme. They do not mean more than a value within one scheme.

The digits are confined to a specific scheme.

They're clearly not. the binary string "11" ("three") uses the exact same configuration of digits as the decimal string "11" ("eleven").

The digit is a representation of a value within the scheme. That string "11" has a different value depending on the scheme it is defined within.

You're making progress. You'd have called that "magical thinking" just yesterday.

You have no point here.

Not according to you: "1/3 is really a rule not a value."

It is a rule saying to divide 1 by 3. That is all 0.33333... is. The product of carrying out the rule. It is not the same thing.

You have included an operation.

The values are subject to the rules of the operation.

Not if the only thing the digit refers to is the digit, then the only applicable operation is concatenation.

The digit in context refers to an abstract value. Nothing more.

You have shown no magical thing behind these digits.

They refer to an abstract value within an abstractly defined scheme. Nothing more.

That's way more than you were willing to admit two days ago, when abstract values where still magical thinking, when the digit and the number were the same thing and a digit could only refer to itself, the digit.

 

[untermensche]

You're making progress. You'd have called that "magical thinking" just yesterday.

Another totally unsupported claim.

What I claim is magical thinking is thinking the "3" in 3 pounds refers to something besides an abstract value within a predefined scheme.

That's way more than you were willing to admit two days ago, when abstract values where still magical thinking, when the digit and the number were the same thing and a digit could only refer to itself, the digit.

I introduced the concept of abstract value.

The exact opposite of what you say here is the truth.

The digit is defined within a specific scheme and within the context of that scheme the digit has an abstract value.

It has nothing else.

 

[Jokodo]

You're making progress. You'd have called that "magical thinking" just yesterday.

Another totally unsupported claim.

What I claim is magical thinking is thinking the "3" in 3 pounds refers to something besides an abstract value within a predefined scheme.

That's way more than you were willing to admit two days ago, when abstract values where still magical thinking, when the digit and the number were the same thing and a digit could only refer to itself, the digit.

I introduced the concept of abstract value.

Others have been calling it number for 3000 years before you realised you also had a need to distinguish the form and meaning of digits. Only when it finally dawned on you that you were hitting a wall with "there are no numbers, digits only refer to themselves" did you introduce numbers through the backdoor by calling them "abstract values".

It's a very transparent maneuver to avoid having to defend an indefensible claim while not directly admitting you were wrong.

 

[Jokodo]

We seem to be in agreement that the strings "1/3", "3/9", "4/12" and "5/15" refers an "abstract value" in the "representational scheme" of fractional notation; that the string "0.333..." refers an "abstract value" in the "representational scheme" of decimal notation; that the string "0.0101..." refers an abstract value in the representational scheme of binary representation; that the string "0.4" refers an abstract value in the representational scheme of duodecimal notation; that the string "0.555..." refers an abstract value in hexadecimal notation.

Maybe we can even agree that they all refer the same abstract value. Given that, it makes little sense to treat that abstract value as an exclusive property of any of those strings. It also follows that having infinitely repeating digits is not a property of that value.

Now you only need to understand that this is what the adults have been talking about all along when they mentioned "numbers", from which again you will understand why "the number (represented by) 0.333... has infinite digits" makes as much sense as saying the animal dog as has three letters.

 

[untermensche]

Another totally unsupported claim.

What I claim is magical thinking is thinking the "3" in 3 pounds refers to something besides an abstract value within a predefined scheme.



I introduced the concept of abstract value.

Others have been calling it number for 3000 years before you realised you also had a need to distinguish the form and meaning of digits. Only when it finally dawned on you that you were hitting a wall with "there are no numbers, digits only refer to themselves" did you introduce numbers through the backdoor by calling them "abstract values".

It's a very transparent maneuver to avoid having to defend an indefensible claim while not directly admitting you were wrong.

My position is clear.

3 is a symbol.

Within a predefined scheme of values it refers to an abstract value.

It refers to nothing more.

Talking about how the position came about is meaningless.

You have not proven 3 is more than a symbol that represents an abstract value within a predefined scheme.

You haven't demonstrated anything but some strange religious ideas.

 

[untermensche]

We seem to be in agreement that the strings "1/3", "3/9", "4/12" and "5/15" refers an "abstract value"

They are idealized values. Values that can never really exist anywhere but the imagination.

But they are also equations that have a product.

And the equation and the product are two distinct entities. They are not the same thing.

Maybe we can even agree that they all refer the same abstract value.

If you start with something like a brick it only has one mass. A mass that can never really be measured to perfection but it can be measured crudely.

So depending on what scheme you use you will get different digits designating the mass of the brick.

These numbers have a tangential relationship in that they refer to the same mass but the digits only refer to an abstract value within a specific predefined scheme of abstract values.

They are not anything more that a symbol that refers to an abstract value within an abstract system of values.

You have not once shown they are anything more than this.

 

[Jokodo]

We seem to be in agreement that the strings "1/3", "3/9", "4/12" and "5/15" refers an "abstract value"

They are idealized values. Values that can never really exist anywhere but the imagination.

But they are also equations that have a product.

And the equation and the product are two distinct entities. They are not the same thing.

Maybe we can even agree that they all refer the same abstract value.

If you start with something like a brick it only has one mass. A mass that can never really be measured to perfection but it can be measured crudely.

So depending on what scheme you use you will get different digits designating the mass of the brick.

These numbers have a tangential relationship in that they refer to the same mass but the digits only refer to an abstract value within a specific predefined scheme of abstract values.

They are not anything more that a symbol that refers to an abstract value within an abstract system of values.

You have not once shown they are anything more than this.

I don't need to. You already admitted that numbers, as abstract entities, exist and are distinct from the digits or digit sequences that refer to them. Your insistence to call them "abstract values" rather than "numbers" doesn't undo that.

Since the number, or if you prefer "abstract value" referred to by the digit sequence "0.333..." doesn't have digits anymore than a dog has letters, your earlier claim that the number is undefined because there is no last digit makes exactly as much sense as talking about furry monosyllabic English animals with four legs.

 

[Jokodo]

Another totally unsupported claim.

What I claim is magical thinking is thinking the "3" in 3 pounds refers to something besides an abstract value within a predefined scheme.



I introduced the concept of abstract value.

Others have been calling it number for 3000 years before you realised you also had a need to distinguish the form and meaning of digits. Only when it finally dawned on you that you were hitting a wall with "there are no numbers, digits only refer to themselves" did you introduce numbers through the backdoor by calling them "abstract values".

It's a very transparent maneuver to avoid having to defend an indefensible claim while not directly admitting you were wrong.

My position is clear.

3 is a symbol.

Within a predefined scheme of values it refers to an abstract value.

It refers to nothing more.

Talking about how the position came about is meaningless.

You have not proven 3 is more than a symbol that represents an abstract value within a predefined scheme.

I haven't claimed more - only that the abstract value can be referred to in multiple ways. Which you already agreed to.

You haven't demonstrated anything but some strange religious ideas.

Pot, meet kettle.

 

[Jokodo]

We seem to be in agreement that the strings "1/3", "3/9", "4/12" and "5/15" refers an "abstract value"

They are idealized values. Values that can never really exist anywhere but the imagination.

That may be so. It isn't relevant to whether they're the same "idealized value"

But they are also equations that have a product.

And the equation and the product are two distinct entities. They are not the same thing.

It appears you're dropping the claim that strings can only have one value.

Maybe we can even agree that they all refer the same abstract value.

If you start with something like a brick it only has one mass. A mass that can never really be measured to perfection but it can be measured crudely.

So depending on what scheme you use you will get different digits designating the mass of the brick.

These numbers have a tangential relationship in that they refer to the same mass but the digits only refer to an abstract value within a specific predefined scheme of abstract values.

They are not anything more that a symbol that refers to an abstract value within an abstract system of values.

You have not once shown they are anything more than this.

You seem to be once again using "numbers" to refer to digits. You don't need to measure the brick 3 times to be able to represent it's mass in 3 notations. You weigh it once at three and a half kg and represent that "abstract value" once as "3.5" in decimal, once as "11.1" in binary, and once as "3.8" in hexadecimal, and if you're so inclined as "3.333..." in base 7. All of these strings refer to the same "abstract value".

 

[fromderinside]

Somebody who will remained unnamed just got whale sized abstract numeric shit dumped on him, eh Jokodo.

BTW from what I read from unnamed, he doesn't account for annual, daily, continuous, confirmations of various instances of weight and measure based on standard procedures and references.

Maybe he thinks he's posting in the philosophy forum.

 

[Jokodo]

Somebody who will remained unnamed just got whale sized abstract numeric shit dumped on him, eh Jokodo.

BTW from what I read from unnamed, he doesn't account for annual, daily, continuous, confirmations of various instances of weight and measure based on standard procedures and references.

Maybe he thinks he's posting in the philosophy forum.

He wouldn't fare any better there with his crude misunderstanding of signs...

 

[untermensche]

I haven't claimed more - only that the abstract value can be referred to in multiple ways. Which you already agreed to.

It is good that you are now admitting you were wrong. Good show.

Yes the symbol points to an abstract value within a specific value scheme.

It points to nothing else.

While in another scheme you would also find digits that do nothing but point to an abstract value within that scheme.

You haven't demonstrated anything but some strange religious ideas.

Pot, meet kettle.

You've just admitted I was right all along.

A digit points to nothing but an abstract value within a predefined scheme.

It points to NOTHING ELSE.

It does not point to another scheme.

 

[Jokodo]

You've just admitted I was right all along.

This cannot logically be correct while contradicting yourself as much as you do..

 

[untermensche]

Find the contradiction.

3 in a symbol that refers to an abstract value within an abstract system of values.

Within that system it is nothing else.

And it does not refer to any other system.