The meaning of infinity

[Artemus]

WOW, That is a lot to digest I really do not see what you are saying. The solution is obvious if you have had diffeq.

The point is that the solution to the differential equation has meaning only under the precise definitions of the mathematical operations used. You deny the validity of those definitions and yet claim that the solutions have meaning. You can't have it both ways.

How so? A Reimann integration is a limut as dx goes to zero. It is an approximation.

No it isn't. It is an exact operation. Please cite any mathematical text or peer reviewed article that says it is an approximation.

 

[untermensche]

Another illustration: All of the following are equivalent labels that can be used to refer to you:

"untermensche"

"the person posting as untermensche at talkfreethought.org"

"untermensche@TFT"

"untermensche, child of <your mothers name> and <your father's name>"

"untermensche, child of <your mother's name> (daughter of <your maternal grandmother's name> and <your maternal grandfather's name>) and <your father's name> (son of <your paternal grandmother's name> and <your paternal grandfather's name>)"

The last can be trivially expanded by including your great-grandparents, and their parents, etc. So there trivially exists a label for you that explicates your genealogy back 32 generations, roughly 1000 years. Pronouncing that label at one second per parent-child relation takes 2 ^ 32 seconds, or 136 years, longer than any human has ever lived. There even exists a label for you that explicates your genealogy back 64 generations, roughly 2000 years. Pronouncing that label would take roughly 40 times the estimated time since the big bang.

By the logic that let's you conclude that the number referred to by 0.(9) "doesn't have a final value" because there exists a label that cannot be actualised, I herewith derive that you don't have a final value, aka don't really exist.

It's either that, or your logic is flawed.

None of those labels refer to me.

I am not some phony name at a chat board.

There is nothing behind the word untermensche. It is a word I made up as far as I know. It refers to no one or no thing. It stands on it's own.

Just like 0.999.... Something humans made up.

 

[untermensche]

Yes.

You end up with infinite strings that cannot possibly end.

The fraction cannot be faithfully represented by the decimal. The decimal is always a little off. Thus the string has no end.

The fraction and the decimal are not the same thing.

Of course they're not. One is a number, the other one is a string, that in a particular language refers to that number. Just like the strings "Australia" and "Asia" refer to continents in the English language. What you're doing is not unlike proclaiming that Australia is more than twice as big as Asia because you did a character count.

There is one language, mathematics, with several dialects.

There are not separate languages.

0.999... does not refer to something.

It is something.

It is something indeed: a string of length eight, with four digits and four punctuation characters.

It is a definition.

It defines a specific entity that is not a translation of any other entity.

There are no magical invisible entities that numbers somehow refer to.

A number is a thing unto itself.

There may be equivalencies but that is not saying it is the same thing.

 

[Jokodo]

There is one language, mathematics, with several dialects.

There are not separate languages.

0.999... does not refer to something.

It is something.

It is something indeed: a string of length eight, with four digits and four punctuation characters.

It is a definition.

What does this even mean?

It defines a specific entity that is not a translation of any other entity.

This may be true in a language you just invented, but it's not true in any language the rest of the world is using to refer to mathematical entities.

Feel free to provide a formal definition of your language so we can evaluate whether it actually is true in your language!

There are no magical invisible entities that numbers somehow refer to.

A number is a thing unto itself.

There may be equivalencies but that is not saying it is the same thing.

You are a bot, aren't you?

You've stopped making sense a while ago, but this right here is a new low.

 

[untermensche]

Dodge.

You are claiming that 0.999... refers to something else.

It does not.

It is an entity unto itself.

 

[Juma]

That wont do. The answer must be a real number. If you cant come up with a real value then the error is EQUAL to 0. That is the definition of equal for reals.

You are not listening, an approximate real number.

Likewise limit x -> inf 1/[2 + 1/x] approaches 2 but never gets there. We take it as 2 in a calculation.

Infinite limits are a tool for analysis, but are nor real.

”Real number” means a point in a the continuum. A element if R, the set of Reals. Not a number for an actual measurement, those will by obvious reasons have finite accuracy.

But I leave you in the same sad abyss of ignirabce as your friend here, untermensche. You have too much arrogance to able to discuss the matter reasonably.. Bye.

 

[DBT]

None of those labels refer to me.

I am not some phony name at a chat board.

There is nothing behind the word untermensche. It is a word I made up as far as I know. It refers to no one or no thing. It stands on it's own.

Just like 0.999.... Something humans made up.

Untermensch;
"Under Man" A term used by the philosopher Friedrich Nietzsche to describe the common man. Likened to sheep, the Untermensch is a social animal spouting pacifist and liberal morality. In this way, he can rationalize his subservience to social and political mores. His existence is solely for the purpose of providing statistical "filler".

 

[Jokodo]

Dodge.

You are claiming that 0.999... refers to something else.

It does not.

It is an entity unto itself.

Not repeating what I've already said and what you've failed to respond to is not a dodge.

https://talkfreethought.org/showthr...ng-of-infinity&p=572496&viewfull=1#post572496
https://talkfreethought.org/showthr...ng-of-infinity&p=572728&viewfull=1#post572728

 

[Jokodo]

Another illustration: All of the following are equivalent labels that can be used to refer to you:

"untermensche"

"the person posting as untermensche at talkfreethought.org"

"untermensche@TFT"

"untermensche, child of <your mothers name> and <your father's name>"

"untermensche, child of <your mother's name> (daughter of <your maternal grandmother's name> and <your maternal grandfather's name>) and <your father's name> (son of <your paternal grandmother's name> and <your paternal grandfather's name>)"

The last can be trivially expanded by including your great-grandparents, and their parents, etc. So there trivially exists a label for you that explicates your genealogy back 32 generations, roughly 1000 years. Pronouncing that label at one second per parent-child relation takes 2 ^ 32 seconds, or 136 years, longer than any human has ever lived. There even exists a label for you that explicates your genealogy back 64 generations, roughly 2000 years. Pronouncing that label would take roughly 40 times the estimated time since the big bang.

By the logic that let's you conclude that the number referred to by 0.(9) "doesn't have a final value" because there exists a label that cannot be actualised, I herewith derive that you don't have a final value, aka don't really exist.

It's either that, or your logic is flawed.

None of those labels refer to me.

I am not some phony name at a chat board.

There is nothing behind the word untermensche. It is a word I made up as far as I know. It refers to no one or no thing. It stands on it's own.

Just like 0.999.... Something humans made up.

Now this is a dodge. Feel free to replace "untermensche" with your real name (and yes, I knew it wasn't your real name). My point stands: There exists a well-defined label for you that is impossible to enumerate in the time since the big bang. There even exists a literally infinite label for you: Once you include downlinks in the genealogy, you run into infinite loops as soon as two parents share a distant ancestor.

The existence of such a label doesn't make you anything other than finite.

 

[untermensche]

None of those labels refer to me.

I am not some phony name at a chat board.

There is nothing behind the word untermensche. It is a word I made up as far as I know. It refers to no one or no thing. It stands on it's own.

Just like 0.999.... Something humans made up.

Untermensch;
"Under Man" A term used by the philosopher Friedrich Nietzsche to describe the common man. Likened to sheep, the Untermensch is a social animal spouting pacifist and liberal morality. In this way, he can rationalize his subservience to social and political mores. His existence is solely for the purpose of providing statistical "filler".

That is Untermensch, not untermensche.

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Dodge.

You are claiming that 0.999... refers to something else.

It does not.

It is an entity unto itself.

Not repeating what I've already said and what you've failed to respond to is not a dodge.

https://talkfreethought.org/showthr...ng-of-infinity&p=572496&viewfull=1#post572496
https://talkfreethought.org/showthr...ng-of-infinity&p=572728&viewfull=1#post572728

I don't respond to research projects.

You are living in a delusion.

0.999... does not refer to anything else.

It is a unique entity unlike any other entity.

If you change it to something else you no longer have it.

 

[untermensche]

Another illustration: All of the following are equivalent labels that can be used to refer to you:

"untermensche"

"the person posting as untermensche at talkfreethought.org"

"untermensche@TFT"

"untermensche, child of <your mothers name> and <your father's name>"

"untermensche, child of <your mother's name> (daughter of <your maternal grandmother's name> and <your maternal grandfather's name>) and <your father's name> (son of <your paternal grandmother's name> and <your paternal grandfather's name>)"

The last can be trivially expanded by including your great-grandparents, and their parents, etc. So there trivially exists a label for you that explicates your genealogy back 32 generations, roughly 1000 years. Pronouncing that label at one second per parent-child relation takes 2 ^ 32 seconds, or 136 years, longer than any human has ever lived. There even exists a label for you that explicates your genealogy back 64 generations, roughly 2000 years. Pronouncing that label would take roughly 40 times the estimated time since the big bang.

By the logic that let's you conclude that the number referred to by 0.(9) "doesn't have a final value" because there exists a label that cannot be actualised, I herewith derive that you don't have a final value, aka don't really exist.

It's either that, or your logic is flawed.

None of those labels refer to me.

I am not some phony name at a chat board.

There is nothing behind the word untermensche. It is a word I made up as far as I know. It refers to no one or no thing. It stands on it's own.

Just like 0.999.... Something humans made up.

Now this is a dodge. Feel free to replace "untermensche" with your real name (and yes, I knew it wasn't your real name). My point stands: There exists a well-defined label for you that is impossible to enumerate in the time since the big bang. There even exists a literally infinite label for you: Once you include downlinks in the genealogy, you run into infinite loops as soon as two parents share a distant ancestor.

The existence of such a label doesn't make you anything other than finite.

I am a real thing.

Any label of me refers to something real.

0.999... does not refer to anything else.

There is no person or thing behind it. It stands alone as a unique expression.

 

[Jokodo]

That is Untermensch, not untermensche.

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Dodge.

You are claiming that 0.999... refers to something else.

It does not.

It is an entity unto itself.

Not repeating what I've already said and what you've failed to respond to is not a dodge.

https://talkfreethought.org/showthr...ng-of-infinity&p=572496&viewfull=1#post572496
https://talkfreethought.org/showthr...ng-of-infinity&p=572728&viewfull=1#post572728

I don't respond to research projects.

You are living in a delusion.

0.999... does not refer to anything else.

It is a unique entity unlike any other entity.

If you change it to something else you no longer have it.

You keep claiming that 0.999... is somehow "not a finite entity". Now, there's two ways to interpret what you mean with "the entity 0.999...":

Either you mean a number. The number commonly referred to as 0.999... is definitely finite - in fact it is no larger than 1.

Or you mean a string. That string is also finite, but it is within the language defined to be a synonym of (=share a referent with) an infinite string (actually two: 1.(0) is just as infinite as 0.(9) and also co-referent).

So the only sense of "0.999..." for which your claim that it is not finite makes even remotely sense is when we're talking about the string used as a label referring to a number.

 

[Jokodo]

Now this is a dodge. Feel free to replace "untermensche" with your real name (and yes, I knew it wasn't your real name). My point stands: There exists a well-defined label for you that is impossible to enumerate in the time since the big bang. There even exists a literally infinite label for you: Once you include downlinks in the genealogy, you run into infinite loops as soon as two parents share a distant ancestor.

The existence of such a label doesn't make you anything other than finite.

I am a real thing.

Any label of me refers to something real.

Oh, but you explained us that an infinite label cannot refer to a finite thing.

You also keep preaching that infinite things cannot exist.

Logically, therefore, if we can show that there's an infinite label for you, you cease to exist.

The fact that you keep spouting your nonsense instead of popping out of existence the moment I defined an infinite label referring to you shows is empirical confirmation that your argument is flawed.

0.999... does not refer to anything else.

There is no person or thing behind it. It stands alone as a unique expression.

Which guy, the string or the number? One of them is not an expression, the other one refers. Your two paragraphs are mutually exclusive as descriptions of the same entity. That's probably the root of your confusion: That you don't distinguish the two.

 

[untermensche]

The number commonly referred to as 0.999... is definitely finite - in fact it is no larger than 1.

It is asymptotic to 1.

It has no final value.

And nobody commonly refers to 1 as 0.999... Nobody would think to do it.

It can be rounded to 1 since it is infinitely close to it and in the real world where decimal places become insignificant quickly there is no difference.

 

[fromderinside]

...except for those who created the convention of limit being at a unitary value.

 

[Jokodo]

The number commonly referred to as 0.999... is definitely finite - in fact it is no larger than 1.

It is asymptotic to 1.

It has no final value.

You keep saying this but you obviously have no idea what an argument for this position might even look like...

And nobody commonly refers to 1 as 0.999... Nobody would think to do it.

And no-one commonly refers to Mexico as "United Mexican States". This doesn't imply that the two labels refer to different things.

 

[untermensche]

...except for those who created the convention of limit being at a unitary value.

That is utility not ultimate truth.

- - - Updated - - -

You keep saying this but you obviously have no idea what an argument for this position might even look like...

It is the way the entity is already defined.

It is defined to have nines without end.

It is defined to never be 1.

 

[Jokodo]

...except for those who created the convention of limit being at a unitary value.

That is utility not ultimate truth.

- - - Updated - - -

You keep saying this but you obviously have no idea what an argument for this position might even look like...

It is the way the entity is already defined.

It is defined to have nines without end.

The string is defined to have 9s without end (or more precisely, to be equivalent to a string with 9s without end).

The number doesn't have any nines. Having or not having a certain sound pattern in its spoken representation, or a certain shape in its written representation, or a certain sequence of 0s and 1s in its representation stored on a machine, is not a possible properties of numbers.

It is defined to never be 1.

You just made this up.

 

[untermensche]

It is the way the entity is already defined.

It is defined to have nines without end.

The string is defined to have 9s without end (or more precisely, to be equivalent to a string with 9s without end).

It is not a statement of equivalence.

It is a uniquely defined entity with unique properties. It does not refer to anything else.

It is defined to never be 1.

You just made this up.

No. I just take the definition seriously and do not abandon it for expedience.

 

[Jokodo]

It is not a statement of equivalence.

It is a uniquely defined entity with unique properties. It does not refer to anything else.

Are you talking about the string or the number?

It is defined to never be 1.

You just made this up.

No. I just take the definition seriously and do not abandon it for expedience.

You take a definition you just made up seriously. Not the one the rest of the world uses.
Here's list of properties of real numbers. e.g.:

13.
Addition Property of Equality
If a = b, then a + c = b + c.

0.999... + 0.999... = 0.999... + 1 = 1.999...

14. Subtraction Property of Equality
If a = b, then a - c = b - c.

0.999... - 0.999... = 0 = 0.999... - 1 = -0