Rational numbers == infinitely repeating sequences of digits

[Jokodo]

The point sailed way above your head.

You have nothing to add here.

As usual.

Either that, or you don't have a point and are too dug in to admit it. I wouldn't want to put my money on the first option.

 

[untermensche]

The point sailed way above your head.

You have nothing to add here.

As usual.

Either that, or you don't have a point and are too dug in to admit it. I wouldn't want to put my money on the first option.

The word Australia has something real behind it. The land was there first then the label attached.

The word three does not.

3 is an invented concept that stands on it's own. It does not represent anything but itself.

Just as 0.3333... does not represent something else.

It represents itself.

And nothing is equivalent to some string of numbers that by definition has no final number in the string, by definition has no final value.

 

[Jokodo]

The point sailed way above your head.

You have nothing to add here.

As usual.

Either that, or you don't have a point and are too dug in to admit it. I wouldn't want to put my money on the first option.

The word Australia has something real behind it. The land was there first then the label attached.

The word three does not.

3 is an invented concept that stands on it's own. It does not represent anything but itself.

Wrong. The "three", the digit "3", the digit sequence "11" interpreted as binary and the digit sequence "2.9..." All Stand for the same number. Whether numbers themselves are real in whatever Sense you have in mind is irrelevant.just like Gandalf is Fiction

Just as 0.3333... does not represent something else.

It represents itself.

And nothing is equivalent to some string of numbers that by definition has no final number in the string, by definition has no final value.

 

[untermensche]

A string of digits repeating infinitely has no final value.

Something with no final value cannot be equivalent to something with a final value.

 

[Jokodo]

A string of digits repeating infinitely has no final value.

Something with no final value cannot be equivalent to something with a final value.

A string of digits does not equal a number it may refer to in whatever system of notation (decimal being as arbitrary as any other). Just like the continent Australia isn't a nine-character-word, and just like the fictional character Gandalf is the same character whichever of his many names he may be referred to by other fictional characters.

This is quite a simple concept really. The continued failure of "untermensche" to understand this simple concept, dully repeating minor variations of one of a couple dozen rote-learnt one-liners instead, is apt to leave the impression that untermensche is in fact a chatbot.

 

[untermensche]

Again. Australia is a label of something real.

"Three" is not.

"Three" is not some other thing the label is pointing to.

It describes nothing else but itself.

It may have some other things it is mathematically similar to but "three" or "3" is only "three" or "3".

It is not something else. There is nothing else for it to be. There is nothing behind the label like "Australia".

 

[Jokodo]

Again. Australia is a label of something real.

"Three" is not.

"Three" is not some other thing the label is pointing to.

It describes nothing else but itself.

It may have some other things it is mathematically similar to but "three" or "3" is only "three" or "3".

It is not something else. There is nothing else for it to be. There is nothing behind the label like "Australia".

It. Does. Not. Matter.

Numbers may or may not be real, under whatever definition of "real" you may have in mind. Things don't need to be real in order to be distinct from their labels. The character Gandalf and the name "Gandalf" are not the same thing despite the fact that both where created the self-same instant by J. R. R. Tolkien. The fact that Gandalf isn't real doesn't make it so that Gandalf and Tharkûn, as he's known to the Dwarves, are distinct entities.

Your argument that "3", "2.9..", "0b11" (i. e., binary 3) and the English word "three" are distinct entities - and must be because one has repeating digits while the others don't - is like saying that Tharkûn and Gandalf are different characters, and must be because one of them contains non-ASCII characters your phone display correctly.

 

[bilby]

The point sailed way above your head.

You have nothing to add here.

As usual.

Either that, or you don't have a point and are too dug in to admit it. I wouldn't want to put my money on the first option.

The word Australia has something real behind it. The land was there first then the label attached.

The word three does not.

3 is an invented concept that stands on it's own. It does not represent anything but itself.

Just as 0.3333... does not represent something else.

It represents itself.

And nothing is equivalent to some string of numbers that by definition has no final number in the string, by definition has no final value.

I don't know what you mean by "final value" in this context; And it is very clear from your posts that neither do you.

It's a placeholder for your desperate desire not to admit that you are wrong; But it's completely meaningless.

 

[untermensche]

If threes repeat without end then no final three can ever be reached.

A final value is never reached. The threes repeat for eternity.

 

[untermensche]

Again. Australia is a label of something real.

"Three" is not.

"Three" is not some other thing the label is pointing to.

It describes nothing else but itself.

It may have some other things it is mathematically similar to but "three" or "3" is only "three" or "3".

It is not something else. There is nothing else for it to be. There is nothing behind the label like "Australia".

It. Does. Not. Matter.

Numbers may or may not be real, under whatever definition of "real" you may have in mind. Things don't need to be real in order to be distinct from their labels. The character Gandalf and the name "Gandalf" are not the same thing despite the fact that both where created the self-same instant by J. R. R. Tolkien. The fact that Gandalf isn't real doesn't make it so that Gandalf and Tharkûn, as he's known to the Dwarves, are distinct entities.

Your argument that "3", "2.9..", "0b11" (i. e., binary 3) and the English word "three" are distinct entities - and must be because one has repeating digits while the others don't - is like saying that Tharkûn and Gandalf are different characters, and must be because one of them contains non-ASCII characters your phone display correctly.

There is something behind the word "Gandalf" even if it is a fictional character.

There is nothing behind the word "three", nothing behind the character "3".

Does the letter "A" refer to something in the world beyond the character?

 

[lpetrich]

As I'd posted earlier, untermensche seems to advocate  finitism. I don't find finitism very convincing, because I don't see any fundamental difference between a rule that generates all the elements of a finite set and one that generates all the elements of an infinite set.

 

[untermensche]

As I'd posted earlier, untermensche seems to advocate  finitism. I don't find finitism very convincing, because I don't see any fundamental difference between a rule that generates all the elements of a finite set and one that generates all the elements of an infinite set.

A rule is not the same thing as the product of the rule.

In fact they are entirely separate.

1/3 is really a rule not a value.

 

[bilby]

If threes repeat without end then no final three can ever be reached.

A final value is never reached. The threes repeat for eternity.

For eternity? But each additional numeral '3' takes zero time to evaluate. So no matter how many there are, it takes zero time to conclude that the decimal is equal to 1/3.

It continues to be clear that you haven't a clue what you are on about.

 

[untermensche]

Thinking about some series of digits has nothing to do with what they are defined as.

Nobody can think 0.3333... into having a final digit.

 

[bilby]

Thinking about some series of digits has nothing to do with what they are defined as.

Nobody can think 0.3333... into having a final digit.

Nobody needs to.

It remains true that it has a value exactly equal to 1/3.

 

[repoman]

Untermensche, could you with moderate training be a university math teacher? Lpetrich easily could from how he rattles off long technical posts.

 

[untermensche]

Thinking about some series of digits has nothing to do with what they are defined as.

Nobody can think 0.3333... into having a final digit.

Nobody needs to.

It remains true that it has a value exactly equal to 1/3.

That is some faith you have but can't reason towards.

To be equal would mean having a final value.

Nothing can be equal to something with no final value.

0.333... by definition has no final value.

You could say 0.333... approaches 1/3 or has 1/3 as a limit though.

We either honor the definition of infinite digits or by caprice ignore it.

But ignoring definitions to suit a desire for completeness is not reasoning.

 

[untermensche]

Untermensche, could you with moderate training be a university math teacher? Lpetrich easily could from how he rattles off long technical posts.

According to him the idea has a pedigree.

I may have invented it for myself but apparently I am not alone.

 

[bilby]

Thinking about some series of digits has nothing to do with what they are defined as.

Nobody can think 0.3333... into having a final digit.

Nobody needs to.

It remains true that it has a value exactly equal to 1/3.

That is some faith you have but can't reason towards.

To be equal would mean having a final value.

Nothing can be equal to something with no final value.

0.333... by definition has no final value.

You could say 0.333... approaches 1/3 or has 1/3 as a limit though.

We either honor the definition of infinite digits or by caprice ignore it.

But ignoring definitions to suit a desire for completeness is not reasoning.

Again with this "final value" crap. WTF is it supposed to mean?

A number has a value. It's value doesn't change over time - if it did, it wouldn't be a number, it would be a variable.

A number has a value. Not a "starting value", an "intermediate value" or a "final value".

 

[untermensche]

That is some faith you have but can't reason towards.

To be equal would mean having a final value.

Nothing can be equal to something with no final value.

0.333... by definition has no final value.

You could say 0.333... approaches 1/3 or has 1/3 as a limit though.

We either honor the definition of infinite digits or by caprice ignore it.

But ignoring definitions to suit a desire for completeness is not reasoning.

Again with this "final value" crap. WTF is it supposed to mean?

It is how infinite digits is defined.

It is digits without the possibility of a last digit.

Digits that go on without end.

A number has a value.

Something that goes on without end cannot have a final value.

0.9999... approaches 1 but it never has a final value so it does not equal 1.