## "0.999... === 1" is at the very least internally consistent

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### Re: "0.999... === 1" is at the very least internally consist

Magnus Anderson wrote:
obsrvr524 wrote:They are actually not.

Words can be redefined to mean anything you want. By redefining the word "square" to mean "circle", the term "square-circle" acquires a different meaning, one that isn't logically contradictory. Similary, by redefining the word "there" to mean the same thing as "here", it becomes logically possible for an object to exist both here and there. But in standard English language, the word "here" and the word "there" are defined as opposites.

No they are not. The only one changing in definitions is you. The word "there" merely means different than "here". "Different" doesn't mean opposite.

The word "here" doesn't have an opposite unless you want to count "not-here" -- which is an idea that YOU keep saying that I have not ever said.

It is only Your assumed ontology of exclusion of presence that demands singular locations of all things. Your ontology is wrong in and for the same reason Newton's ontology was wrong.

But why are you arguing pedantic wording when you obviously know what I mean.

Magnus Anderson wrote:

You're missing the point. I am well aware of the fact that you never explicitly said "P and not-P". My claim is that you did so implicitly. People often say things without being aware of their implications.

You should know by now that I do not play word games. Your implied conclusion is flawed. "Here and also there" does NOT mean "here but not-here" or "P but not-P". If anyone is redefining anything it is you (and wouldn't be the first time).

Magnus Anderson wrote:They are not merely saying "We define the word 'gender' in a different way". That wouldn't have been a problem.

Of course they don't say it - then it wouldn't be a problem that couldn't be settled. Not settling the problem is a part of the game - solutions are not allowed (much like philosophy).

Magnus Anderson wrote:They are actually trying to change everyone's vocabulary by telling them they are defining the word "gender" in the wrong way. One way they do it is by employing postmodern philosophy e.g. by claiming that no portion of reality can be accurately represented using binary terms. As an example, you can't say that someone's hair is either gray or not gray because everyone's hair has both light and dark areas. It's all a consequence of an excessively materialistic / concretistic way of thinking.

Their method is one of creating confusion and contention ("divide and conquer"). You are helping them by not understanding that. They are not going to define their words - but simply tell you that you are wrong and a bad person for not following their holy virtuous truth. They hope to be able to inspire one group to hate the other group by omitting the definitions of their words. You and I know to define our words (or at least make an attempt). Most people by far - do not know that. Those people get insanely angry and hate you without ever realizing that it was all just a trick of words = politics.

Magnus Anderson wrote:A part is what something is composed of. The word "portion" normally means the same exact thing -- but I'm not sure what you mean by it.

Okay if you mean the exact same thing as "portion" (rather than "particulate" - where "part" came from) then you are most emphatically wrong - and provably so.

Magnus Anderson wrote:A thing that isn't composed of anything has zero parts and is nothing at all. A thing that is composed of one thing has one part is an indivisible thing.

That is where you are wrong. There is no such thing in the physical universe as a portion that cannot be subdivided. The universe is NOT made of particulate components (as evidenced by matter-anti-matter annihilation). Also simple geometry demonstrates that it is impossible to have minimum lengths - the universe would have to become crystalline and probably locked up on itself.
You have been observed.
Though often tempted to encourage a dog to distinguish color I refuse to argue with him about it
It's just the same Satanism as always -
• separate the bottom from the top,
• the left from the right,
• the light from the dark, and
• blame each for the sins of the other
• - until they beg you to take charge.
• -- but "you" have been observed --

The prospect of death weighs naught upon the purpose of life - James S Saint - 2009
obsrvr524
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### Re: "0.999... === 1" is at the very least internally consist

Magnus Anderson wrote:
origami wrote:If 5 minutes is infinitely divisible, it only means that there is no minimum point.

"No minimum point" means that it's nothing at all.

If that is the case then definitely "1 = 0.999..."

But that isn't the case because subdividing can never get to zero - there is always a remainder.

This is why I asked long ago about "1 / (absolute infinity)" -- you said you don't see the relevance. This is the relevance.
You have been observed.
Though often tempted to encourage a dog to distinguish color I refuse to argue with him about it
It's just the same Satanism as always -
• separate the bottom from the top,
• the left from the right,
• the light from the dark, and
• blame each for the sins of the other
• - until they beg you to take charge.
• -- but "you" have been observed --

The prospect of death weighs naught upon the purpose of life - James S Saint - 2009
obsrvr524
Philosopher

Posts: 4238
Joined: Thu Jul 11, 2019 9:03 am

### Re: "0.999... === 1" is at the very least internally consist

obsrvr524 wrote:The word "there" merely means different than "here". "Different" doesn't mean opposite.

That's what matters. They are different. If "here" and "there" are different locations, it follows that "there" is a different location from "here" i.e. that "there" is not "here". Thus, when you say "It's here and there", you are saying "It's here and not here". That's all I've been saying. You may be right that "here" and "there" are not opposites but that has no impact on my argument.

You should know by now that I do not play word games.

Yes, you do.

Okay if you mean the exact same thing as "portion" (rather than "particulate" - where "part" came from) then you are most emphatically wrong - and provably so.

Feel free to demonstrate it.

That is where you are wrong. There is no such thing in the physical universe as a portion that cannot be subdivided. The universe is NOT made of particulate components (as evidenced by matter-anti-matter annihilation). Also simple geometry demonstrates that it is impossible to have minimum lengths - the universe would have to become crystalline and probably locked up on itself.

Instead of distracting yourself by looking at popular theories, feel free to prove that it's conceptually possible for a thing that is composed of no more than one part to be divided into an infinite number of parts.
Magnus Anderson
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### Re: "0.999... === 1" is at the very least internally consist

obsrvr524 wrote:If that is the case then definitely "1 = 0.999..."

Not at all. Again, feel free to prove it.

But that isn't the case because subdividing can never get to zero - there is always a remainder.

If something is infinitely divisible, it merely means it can be split / divided into an infinite number of things. It's not implied that there is no smallest portion of it.

An example is an infinite queue of indivisible objects e.g. {1, 2, 3, ...} You can infinitely divide it even though it's composed of indivisible objects. For example, you can divide it into {1}, {2}, {3}, etc. What's causing the confusion is the unobserved fact that a thing can be cut into more than one way. The same set can be cut by splitting it into two halves and then each half into two halves and so on. In this case, you will never reach the smallest element, not because it doesn't exist, but because of the way you're slicing the object. Your first division may result in {1, 3, 5, ...} and {2, 4, 6, ...}. Your second may result in {1, 5, 9, ...}, {3, 7, 11, ...}, {2, 6, 10, ...}, {4, 8, 12, ...}. And so on. There is no end to this process. Does that mean there is no smallest element? Of course not.
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### Re: "0.999... === 1" is at the very least internally consist

Magnus Anderson wrote:
obsrvr524 wrote:The word "there" merely means different than "here". "Different" doesn't mean opposite.

That's what matters. They are different. If "here" and "there" are different locations, it follows that "there" is a different location from "here" i.e. that "there" is not "here". Thus, when you say "It's here and there", you are saying "It's here and not here". That's all I've been saying. You may be right that "here" and "there" are not opposites but that has no impact on my argument.

Now You are conflating the language of logic --
"not-P" = "anything other than P" or "the absence of P" - the negation of P?

"not here" means that "it isn't here" - after I already said it IS here.

I'm talking inclusive terms and you keep injecting exclusive terms (leave out the negatives - "not").

It is BOTH "here" and also "there" too.

Magnus Anderson wrote:
You should know by now that I do not play word games.

Yes, you do.

BS (strike 1).

Magnus Anderson wrote:
Okay if you mean the exact same thing as "portion" (rather than "particulate" - where "part" came from) then you are most emphatically wrong - and provably so.

Feel free to demonstrate it.

If you would get off of your twisting pedantics we might.

Magnus Anderson wrote:
That is where you are wrong. There is no such thing in the physical universe as a portion that cannot be subdivided. The universe is NOT made of particulate components (as evidenced by matter-anti-matter annihilation). Also simple geometry demonstrates that it is impossible to have minimum lengths - the universe would have to become crystalline and probably locked up on itself.

Instead of distracting yourself by looking at popular theories, feel free to prove that it's conceptually possible for a thing that is composed of no more than one part to be divided into an infinite number of parts.

By your definition of "part" there is no such thing as "a thing composed of only one part/portion". It doesn't exist in the physical universe. Energy doesn't come in particulates except in quantum mechanics where it is understood to be only the maths of averaged quantities - quanta.
You have been observed.
Though often tempted to encourage a dog to distinguish color I refuse to argue with him about it
It's just the same Satanism as always -
• separate the bottom from the top,
• the left from the right,
• the light from the dark, and
• blame each for the sins of the other
• - until they beg you to take charge.
• -- but "you" have been observed --

The prospect of death weighs naught upon the purpose of life - James S Saint - 2009
obsrvr524
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Joined: Thu Jul 11, 2019 9:03 am

### Re: "0.999... === 1" is at the very least internally consist

obsrvr524 wrote:"not here" means that "it isn't here" - after I already said it IS here.

Johnny said he's tall and short. "Short" means "not tall". Therefore, he said he's tall and he also said he's not tall. That's a contradiction. A logical contradiction is a state in which someone holds two mutually exclusive beliefs at the same time i.e. B and not-B. In Johnny's case, these are "Johnny is tall" and "Johnny is not tall". In your case, these are "This object is at location L" and "This object is not at location L". "Here" and "there" refer to two different locations. You said it yourself. This means that "there" is not "here" and that "here" is not "there". If we use "L" to refer to "here", then "You are here and there" means "You are at location L and you are not at location L". It's a textbook example of logical contradiction.

I'm talking inclusive terms and you keep injecting exclusive terms (leave out the negatives - "not").

It is BOTH "here" and also "there" too.

Yes, and Johnny says he's BOTH a man AND a woman. According to you, that is totally not equivalent to "Johnny is both a man and not a man", because Johnny didn't use those words, he used different ones. He didn't speak in exclusive terms, he spoke in inclusive ones. That totally means he's not contradicting himself.

A logical contradiction is a conjunction of statement P and its opposite not-P but almost never in an explicit form where it can be easily seen for what it is. It most commonly comes in the form of "It's A and B" where "B" means "not A" but without the author being aware of it. He's speaking in inclusive terms too but he's nonetheless contradicting himself.

BS (strike 1).

I asked you to define the word "vagueness" and what happened? You made a number of failed attempts and then you simply abandoned the project.
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### Re: "0.999... === 1" is at the very least internally consist

Magnus Anderson wrote:
origami wrote:If 5 minutes is infinitely divisible, it only means that there is no minimum point.

"No minimum point" means that it's nothing at all.

You seriously have still not demonstrated why. You arbitrarily invent points. I arbitrarily invent a string.Points are particles. String is a continuum. Both can be imagined as physical objects with mass. You can divide a string indefinitely, because there will always be a stretch of string left.

But aside from this. If your concept requires an absurdity, as you have said, then it is a bad concept. Yours contains an absurdity. A square circle. And the absurdity is that a given finite quantity, if added to itself infinitely, will have a finite quantity.
There's no one thing that's true. It's all true.
Ernest Hemingway

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### Re: "0.999... === 1" is at the very least internally consist

I think I can understand obsrever's comments on Zeno's paradox like this:

If you add a finite quantity to itself infinitely, all lines will be crossed. This is evident, the addition will eventually equal any possible number, 1, 1 million, 1 million times one million times one quatridillion. All of these will be met in the infinite progression, as well as any other.

For this to be avoided, the only thing that can be added to itself infinitely and still not reach a given finite quantity is 0, because no matter how many times you add it to itself, the result will be 0.

He then says, as I understand him, that this means that if the universe is composed of 0points, then nothing could ever happen because the chain of 0's would never be broken and any given quantity never arrived at. But I already think this is conceding too much. The actuality is that 0 cannot be a point, by virtue of representing no quantity of points. There is actually no problem in overcoming infinite 0's. It simply says nothing about what is beyond the zero's, neither by way of proof or disproof. If what lies beyond is minimum points or strings or something else entirely, an infinite progression of 0's says nothing about it one way or the other. Meaningless.
There's no one thing that's true. It's all true.
Ernest Hemingway

origami
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### Re: "0.999... === 1" is at the very least internally consist

Magnus Anderson wrote:
obsrvr524 wrote:"not here" means that "it isn't here" - after I already said it IS here.

Johnny said he's tall and short. "Short" means "not tall".

- The light is shining here and there.
- Why?
= Because "here" and "there" are opposites - if it is here it is not there.
- It is shining in BOTH places - both HERE and also there - nothing contradictory.

Magnus Anderson wrote:I asked you to define the word "vagueness" and what happened? You made a number of failed attempts and then you simply abandoned the project.

What is the definition of insanity? - at some point - a sane person stops.
---
When someone obviously doesn't want to know the answer to the question he asked - I stop bothering to make him make excuses for avoiding his own understanding.
---

To the issue of the impossibility of a minimum length --

Imagine you have a line segment that is exactly the proper number of minimum lengths to go from point A to point B along the X-axis. And to make it clear - the line goes from the left edge of point A down the X-axis to the left edge of point B - an exact number of minimal lengths.

Now if you choose to go from point A to the next minimal distance point that is directly above B - that is impossible. In fact there are an infinity of possible angles to choose to get directly above B - yet not one that will allow the line to end at a point perfectly directly above B. And there is actually only one that will allow the line to end at any pre-specified point above the X axis between A and B.

A minimum length requires that right triangle motion is impossible (and a great many other common motions).

origami wrote:I think I can understand obsrever's comments on Zeno's paradox like this:

If you add a finite quantity to itself infinitely, all lines will be crossed. This is evident, the addition will eventually equal any possible number, 1, 1 million, 1 million times one million times one quatridillion. All of these will be met in the infinite progression, as well as any other.

For this to be avoided, the only thing that can be added to itself infinitely and still not reach a given finite quantity is 0, because no matter how many times you add it to itself, the result will be 0.

He then says, as I understand him, that this means that if the universe is composed of 0points, then nothing could ever happen because the chain of 0's would never be broken and any given quantity never arrived at.

Yes - that was one of the points I tried to get across.

origami wrote:But I already think this is conceding too much. The actuality is that 0 cannot be a point, by virtue of representing no quantity of points. There is actually no problem in overcoming infinite 0's. It simply says nothing about what is beyond the zero's, neither by way of proof or disproof. If what lies beyond is minimum points or strings or something else entirely, an infinite progression of 0's says nothing about it one way or the other. Meaningless.

I understood your argument there as well. I was just watching to see who made any headway.
You have been observed.
Though often tempted to encourage a dog to distinguish color I refuse to argue with him about it
It's just the same Satanism as always -
• separate the bottom from the top,
• the left from the right,
• the light from the dark, and
• blame each for the sins of the other
• - until they beg you to take charge.
• -- but "you" have been observed --

The prospect of death weighs naught upon the purpose of life - James S Saint - 2009
obsrvr524
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Posts: 4238
Joined: Thu Jul 11, 2019 9:03 am

### Re: "0.999... === 1" is at the very least internally consist

-
Another issue concerning the minimal length hypothesis is more relevant to my squaring the circle study --

If any diameter for a circle is formed by any finite number of minimum lengths (and all lengths would have to qualify) - it would then be impossible to draw a circle with that diameter. If the diameter of a circle is a rational number (and all lengths would have to qualify as rational) the circumference is necessarily and always irrational.

Being irrational means that the circumference of every circle would have to include a fractional minimal length - else be incomplete. Pi and any rational portion of Pi could never be achieved - circles could never be drawn.
You have been observed.
Though often tempted to encourage a dog to distinguish color I refuse to argue with him about it
It's just the same Satanism as always -
• separate the bottom from the top,
• the left from the right,
• the light from the dark, and
• blame each for the sins of the other
• - until they beg you to take charge.
• -- but "you" have been observed --

The prospect of death weighs naught upon the purpose of life - James S Saint - 2009
obsrvr524
Philosopher

Posts: 4238
Joined: Thu Jul 11, 2019 9:03 am

### Re: "0.999... === 1" is at the very least internally consist

obsrvr524 wrote:- The light is shining here and there.
- Why?
= Because "here" and "there" are opposites - if it is here it is not there.
- It is shining in BOTH places - both HERE and also there - nothing contradictory.

Yeah, there's nothing contradictory about that. But that's not what you're saying. What you're saying is that a particle is both here and there at the same time. And you're not merely saying "It's occupying multiple different points at the same time" for that would be a banality everyone is aware of. You don't need to be a physicists to know that. Boris Johnson, for example, occupies who knows how many points in space. He does not occupy a single point for that would make him the smallest person in the world -- which clearly he is not. He occupies many regions of space, and for that reason, many points as well. What you're saying is that one and the same point belonging to a particle is located at two different points in space. And THAT is a contradiction.

What is the definition of insanity? - at some point - a sane person stops.
---
When someone obviously doesn't want to know the answer to the question he asked - I stop bothering to make him make excuses for avoiding his own understanding.

I don't care about your justifications. You're still here, talking to me. You didn't leave. If you left, that would be fine by me. Instead, you changed the direction of our conversation.
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### Re: "0.999... === 1" is at the very least internally consist

origami wrote:You seriously have still not demonstrated why.

That much is obvious. I will give it a try another time.

But aside from this. If your concept requires an absurdity, as you have said, then it is a bad concept. Yours contains an absurdity. A square circle. And the absurdity is that a given finite quantity, if added to itself infinitely, will have a finite quantity.

Forgive me if I'm not following you, but as it seems, you are not really addressing something I've said. You seem to be saying that if it's logically necessary for the smallest region of time to exist, that it's impossible for one second to be infinitely divisible. That may or may not be true. Actually, I don't agree with it, but that's not something I recently said. My claim is merely that it's logically necessary for the smallest region of time to exist. What follows from that is a separate story. But now that you mentioned that . . .

. . . that brings us back to what we argued at the beginning. When you say that "second" is "finite", you mean it has a beginning and an end. Right? That's what you mean. But if a sequence has a beginning and an end, is it necessarily composed of an infinite number of elements? In other words, is $$(2, 3, 4, \dotso, 1)$$ a logical impossibility? I see no reason why that would be the case. Feel free to argue otherwise.
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### Re: "0.999... === 1" is at the very least internally consist

Here's an attempt.

origami wrote:You seriously have still not demonstrated why.

To divide, or split, a thing is to take some or all of its parts and separate them. In spatial terms, to separate a collection of things often means to increase the distance between them. That's a definition. I think we are in agreement so far.

A thing that is composed of no parts is nothing, and therefore, it cannot be divided. There are no parts to separate. A part that is composed of no more than one part is also impossible to divide because there is only one part and no other part to separate that part from. What that means is that, in order to divide a thing, it must consist of at least two parts.

Is a period of time we call "second" nothing at all? If so, then seconds cannot be divided at all, for there is nothing to divide.

Is second a kind of thing that is made out of no more than one part? If so, that would make it indivisible. An indivisible thing cannot be divided at all.

Is second made out of more than one part? If so, it's a divisible thing.

I am sure that you will go with #3 i.e. that seconds are divisible things. What that means is that seconds are composed of more than one part. They aren't nothing, they aren't atomic moments . . . they are a collection of things.

Since seconds are collections of things, can you tell us a bit about what kind of collections they are e.g. what kind of elements they are made of, how many elements there are, etc.

An average person would say something like "Sure! A second is composed of 1,000 milliseconds!" Great. I think that's a decent start. But what about these milliseconds? What kind of things are they? Are they a collection of things too? Or are they singular? "A millisecond is made out of 1,000 microseconds!" Wow, so they are collections too! I bet microseconds are collections just as well. "That happens to be right. It's a collection containing 1,000 collections each containing 1,000 collections and so on with no end in sight!"

Basically, what the above is saying is that time is a collection consisting of collections consisting of collections and so on ad infinitum. Unless the above person meant that these collections are made out of indivisible elements -- and he didn't tell us that -- it tells us nothing at all. In fact, he might as well be describing non-existence. You can describe "nothing" using the same exact statement.

A collection that is made out of collections, regardless of how deeply nested, but that has no singular elements, at any level, is an empty collection. In other words, it's nothing at all.
Last edited by Magnus Anderson on Mon Jul 04, 2022 6:46 pm, edited 1 time in total.
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### Re: "0.999... === 1" is at the very least internally consist

Magnus Anderson wrote:
origami wrote:You seriously have still not demonstrated why.

That much is obvious. I will give it a try another time.

But aside from this. If your concept requires an absurdity, as you have said, then it is a bad concept. Yours contains an absurdity. A square circle. And the absurdity is that a given finite quantity, if added to itself infinitely, will have a finite quantity.

Forgive me if I'm not following you, but as it seems, you are not really addressing something I've said. You seem to be saying that if it's logically necessary for the smallest region of time to exist, that it's impossible for one second to be infinitely divisible. That may or may not be true. Actually, I don't agree with it, but that's not something I recently said. My claim is merely that it's logically necessary for the smallest region of time to exist. What follows from that is a separate story. But now that you mentioned that . . .

. . . that brings us back to what we argued at the beginning. When you say that "second" is "finite", you mean it has a beginning and an end. Right? That's what you mean. But if a sequence has a beginning and an end, is it necessarily composed of an infinite number of elements? In other words, is $$(2, 3, 4, \dotso, 1)$$ a logical impossibility? I see no reason why that would be the case. Feel free to argue otherwise.

It may or may not be that you said it. In an attempt to see where we stand, I will put forward some postulations, and draw conclusions. You can tell me whether we agree on those conclusions, or if you see flaws in the postulations:

Time may or may not be infinitely divisible.

Time may or may not be composed of points that constitute the minimum possible quantity of time.

For any point of time to exist, it must be said to have quantity. Redundantly, it cannot be 0.

Any point of time above 0 will, if added to itself infinitely, eventually surpass every possible finite measure of time, whether that be one second, five minutes, or any other finite measure.

If there exist a point of time which constitutes a minimum possible quantity of time, a finite stretch of time cannot be infinitely divisible.

If there exist no minimum possible quantity of time, a finite stretch of time may be infinitely divisible.
Last edited by origami on Mon Jul 04, 2022 6:54 pm, edited 2 times in total.
There's no one thing that's true. It's all true.
Ernest Hemingway

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### Re: "0.999... === 1" is at the very least internally consist

Magnus Anderson wrote:Here's an attempt.

origami wrote:You seriously have still not demonstrated why.

To divide, or split, a thing is to take some or all of its parts and separate them. In spatial terms, to separate a collection of things often means to increase the distance between them. That's a definition. I think we are in agreement so far.

Not quite.

To divide, or split, a thing is to transform it from one part into more than one part, all of the parts made only and completely of the constituents of the original part.

In other words, a division doesn't require parts to be preexisting, but can create parts.

What I do agree with is that it is possible for a thing no longer to be divisible, so that no new parts can be created by splitting.
There's no one thing that's true. It's all true.
Ernest Hemingway

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### Re: "0.999... === 1" is at the very least internally consist

origami wrote:Time may or may not be infinitely divisible.

Agree.

Time may or may not be composed of points that constitute the minimum possible quantity of time.

I don't agree with that. I think that the smallest possible period of time is a logical necessity.

For any point of time to exist, it must be said to have quantity. Redundantly, it cannot be 0.

Agree. That's another way of saying it must be composed of at least one part.

Any point of time above 0 will, if added to itself infinitely, eventually surpass every possible finite measure of time, whether that be one second, five minutes, or any other finite measure.

Assuming you're saying no more than "Infinity is larger than every integer", I agree.

If there exist a point of time which constitutes a minimum possible quantity of time, time cannot be infinitely divisible.

It's a bit unclear what you're saying here. There are possibilities with one possibility being more likely.

"Infinitely divisible" merely means "can be divided / split into an infinite number of parts". Anything that is made out of an infinite number of parts is infinitely divisible. The set of natural numbers, for example, is infinitely divisible. I am assuming this is not what you're saying.

My guess is that what you're saying is the following:

1) From our observation, we can all tell that every period of time eventually comes to an end.

2) If time consists of an infinite number of indivisible moments, then no period of time can come to an end because it would take infinity to complete it i.e. it would never be completed.

3) Thus, if (3) is true, it follows that time isn't infinitely divisible.

I don't agree with the second premise.

If there exist no minimum possible quantity of time, time may be infinitely divisible.

I disagree because "no minimimum possible quantity of time" means there is no time at all. Thus, there is nothing to divide -- finitely or infinitely.
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### Re: "0.999... === 1" is at the very least internally consist

Magnus Anderson wrote:I disagree because "no minimimum possible quantity of time" means there is no time at all. Thus, there is nothing to divide -- finitely or infinitely.

Before we get to that, let's rule out the absurdity.

Magnus Anderson wrote:
If there exist a point of time which constitutes a minimum possible quantity of time, time cannot be infinitely divisible.

It's a bit unclear what you're saying here. There are possibilities with one possibility being more likely.

I edited the post afterwwards to correct a small mistake. It should read like this:

"If there exist a point of time which constitutes a minimum possible quantity of time, a finite stretch of time cannot be infinitely divisible."

What I am saying is that, if a minimum point of time has quantity, and if that quantity added to itself will eventually add up to every possible measure of time before it ceases to be endless, infinite, then it logically follows that by the time it reaches 1 second, it will be a finite number of minimum possible points of time, and that, consequently, that second will not be infinitely divisible.
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origami
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### Re: "0.999... === 1" is at the very least internally consist

origami wrote:Not quite.

To divide, or split, a thing is to transform it from one part into more than one part, all of the parts made only and completely of the constituents of the original part.

In other words, a division doesn't require parts to be preexisting, but can create parts.

That sounds more like multiplication rather than division. In multiplication, such as that of reproduction, you have a thing (a woman) from which a number of new things are created (babies.) The new things (babies) aren't parts of the original thing (woman). They are separate things.

But you are right in that you can look at the process of division through this lens as well. You can say that cutting an apple into two halves produces two new things -- the two halves that are different from the original apple. This isn't invalid, it's merely a different way of representing reality. But it's not the only way to do it. You can also say the resulting pieces are parts of the original apple separated physically. There's absolutely nothing incorrect about that either.
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### Re: "0.999... === 1" is at the very least internally consist

obsrvr524 wrote:To the issue of the impossibility of a minimum length --

Imagine you have a line segment that is exactly the proper number of minimum lengths to go from point A to point B along the X-axis. And to make it clear - the line goes from the left edge of point A down the X-axis to the left edge of point B - an exact number of minimal lengths.

Now if you choose to go from point A to the next minimal distance point that is directly above B - that is impossible. In fact there are an infinity of possible angles to choose to get directly above B - yet not one that will allow the line to end at a point perfectly directly above B. And there is actually only one that will allow the line to end at any pre-specified point above the X axis between A and B.

A minimum length requires that right triangle motion is impossible (and a great many other common motions).

obsrvr524 wrote:-
If any diameter for a circle is formed by any finite number of minimum lengths (and all lengths would have to qualify) - it would then be impossible to draw a circle with that diameter. If the diameter of a circle is a rational number (and all lengths would have to qualify as rational) the circumference is necessarily and always irrational.

Being irrational means that the circumference of every circle would have to include a fractional minimal length - else be incomplete. Pi and any rational portion of Pi could never be achieved - circles could never be drawn.

Minimum lengths and durations are logically irrational - as noted above.
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### Re: "0.999... === 1" is at the very least internally consist

Magnus Anderson wrote:You can also say the resulting pieces are parts of the original apple separated physically. There's absolutely nothing incorrect about that either.

No! An apple is 1 whole apple, not 2 half apples. The ONLY way to get two half apples from 1 whole apple is to DIVIDE the whole apple into 2 half apples.

If you claim 1.0 apple is actually 2 1/2 apples added together, then you must also be claiming that an apple is 4 1/4 apples, and 8 1/8 apples, and 16 1/16 apples all at the same time.

That is ABSURD to claim 1.0 whole apple is the addition of fractional apple parts, and move the goal post for every different number of parts. That is OUTRAGEOUS!

What you are doing is claiming 1.0 apple is made up of parts of 1.0 apple, and then changing the number of parts for every different scenario. You are saying an apple is made up of the number of parts that suite your fancy. (rolls eyes)

If I have 1.0 apple and I divide it into 2 parts, how many parts is each half made up of, 4? You're saying a half an apple is made up of 4 parts of 1/8, and 8 parts of 1/16, and 64 parts of 1/128 at the same time?

So what about the other half, how many parts is that made up of?

Are you saying 1.0 apple is really 4 parts of 1/8, and 8 parts of 1/16 added together? So a total of 12 parts of what?

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### Re: "0.999... === 1" is at the very least internally consist

Motor Daddy wrote:No! An apple is 1 whole apple, not 2 half apples. The ONLY way to get two half apples from 1 whole apple is to DIVIDE the whole apple into 2 half apples.

I suppose you're not made out of cells, then?

If you claim 1.0 apple is actually 2 1/2 apples added together, then you must also be claiming that an apple is 4 1/4 apples, and 8 1/8 apples, and 16 1/16 apples all at the same time.

That's correct.

You're saying a half an apple is made up of 4 parts of 1/8, and 8 parts of 1/16, and 64 parts of 1/128 at the same time?

Exactly. There is any number of mutually compatible and correct ways that reality can be described. There isn't only one. That's why there are multiple languages, not just one.
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### Re: "0.999... === 1" is at the very least internally consist

origami wrote:What I am saying is that, if a minimum point of time has quantity, and if that quantity added to itself will eventually add up to every possible measure of time before it ceases to be endless, infinite, then it logically follows that by the time it reaches 1 second, it will be a finite number of minimum possible points of time, and that, consequently, that second will not be infinitely divisible.

I am not following you. How can an infinite addition of indivisible things ever become a finite number of indivisible things?
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### Re: "0.999... === 1" is at the very least internally consist

Flannel Jesus - Science, Tech, and Math Rules wrote:3:
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This is how discussions deteriorate.
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### Re: "0.999... === 1" is at the very least internally consist

Well, at least someone noticed (:
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### Re: "0.999... === 1" is at the very least internally consist

Magnus Anderson wrote:
origami wrote:What I am saying is that, if a minimum point of time has quantity, and if that quantity added to itself will eventually add up to every possible measure of time before it ceases to be endless, infinite, then it logically follows that by the time it reaches 1 second, it will be a finite number of minimum possible points of time, and that, consequently, that second will not be infinitely divisible.

I am not following you. How can an infinite addition of indivisible things ever become a finite number of indivisible things?

For example, 1(indivisible thing) + 1 = 2.

There we have 2 indivisible things, a finite number.

Since your indivisible points of time have quantity, continuing the process indefinitely (2 + 1, 3 + 1, 4 + 1, ... ) will eventually give whatever finite quantity of time you have chosen (5 minutse, for example) before reaching infinity, which is a contradiction in terms.

What this means is that any addition process of any fixed quantity that gives any other finite quantity must necessarily be a finite process.

The infinite addition keeps progressing, but the finite quantity you were adding up to (5 minutes, for example) lays somewhere within a finite iteration of that infinite process.
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