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

For discussing anything related to physics, biology, chemistry, mathematics, and their practical applications.

Moderator: Flannel Jesus

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

Postby Magnus Anderson » Fri Jul 01, 2022 11:53 pm

Motor Daddy wrote:No. What is flawed in Zeno's BS is that 1.0 is not made up of 1/2+1/4+1/8+1/16... That will NEVER equal 1.0! It is a flawed concept from the start. It is almost like saying 1 step forward and 2 steps backwards is the method to get there, but it doesn't add up! 1 step forward and 2 steps backwards is POSSIBLE, but it will not get you to the 1.0 mile marker, just as 1/2 + 1/4 + 1/8... will not get you there. It is total NONSENSE, just like 1 step forward and 2 steps backwards is total nonsense!


While that's true, it's not the gist of Zeno's dichotomy paradox. His paradox is also accompanied by the conclusion that you can't even start moving because there is no immediately adjacent point to the one you're starting from. In other words, in order to change your position to any other position, you have to cross an endless number of positions in between. And that's not possible because "endless" means "no end". So it doesn't really matter how you're going to move towards your destination. You can't even start moving according to Zeno.
Magnus Anderson
ILP Legend
 
Posts: 6117
Joined: Mon Mar 17, 2014 7:26 pm

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

Postby origami » Sat Jul 02, 2022 12:19 am

Magnus Anderson wrote:From there, it's easy to deduce that a set of elements is said to be infinitely divisible if it can be split into an infinite number of non-empty sets. \(\{1, 2\}\) is clearly not infinitely divisible but the set of all natural numbers \(\{1, 2, 3, \dotso\}\) is because you can split it into \(\{1\}\), \(\{2\}\), \(\{3\}\) and so on.

See? We just infinitely divided a set and ended up with indivisible sets.


What you did was posit the addition of an infinite amount of finite elements, and then the division of the infinite set. You did not posit infinite division of a finite set, meaning that time is only infinitely divisible, according to these standards, if it is infinitely long. No actual stretch of time is infinitely divisibe.
There's no one thing that's true. It's all true.
Ernest Hemingway
User avatar
origami
Philosopher
 
Posts: 2313
Joined: Wed Jun 15, 2022 2:47 pm

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

Postby origami » Sat Jul 02, 2022 12:24 am

In other words, all of time from right now to all of eternity, {1,2,3,...} is infinitely divisible, but all of time from here until five minutes from now {1,...,x}, where "..." is used to reprsent the finite number of individual points between now and 5 minutes from now, represented by x, is not infinitely divisible. We know, because five minutes is a finite stretch, and we have agreed that the minimum possible point in this system must also be a finite quantity, so that an infinite amount of them would surpass 5 minutes.
There's no one thing that's true. It's all true.
Ernest Hemingway
User avatar
origami
Philosopher
 
Posts: 2313
Joined: Wed Jun 15, 2022 2:47 pm

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

Postby Magnus Anderson » Sat Jul 02, 2022 12:27 am

origami wrote:You did not posit infinite division of a finite set


Yes, I didn't, and I didn't because it's logically impossible. Can you split \(\{1, 2, 3\}\), or any other finite set, into an infinite number of non-empty sets? There aren't enough elements, right? So you can't actually do. It's like dividing \(\{1\}\) into \(3\) non-empty sets. You can't do it.
Magnus Anderson
ILP Legend
 
Posts: 6117
Joined: Mon Mar 17, 2014 7:26 pm

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

Postby origami » Sat Jul 02, 2022 12:37 am

That is my point. Any given stretch of time that is not itself infinite cannot contain an infinite amount of finite points. By definition. No matter how small the quantity of the minimum point is, if it is an existing quantity, it will eventually add up to the entirety of the strech of time, and thus clearly not be infinite.
There's no one thing that's true. It's all true.
Ernest Hemingway
User avatar
origami
Philosopher
 
Posts: 2313
Joined: Wed Jun 15, 2022 2:47 pm

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

Postby origami » Sat Jul 02, 2022 1:04 am

Finite stretches of time can only be posited to be infinitely divisible if they are not composed of points.
There's no one thing that's true. It's all true.
Ernest Hemingway
User avatar
origami
Philosopher
 
Posts: 2313
Joined: Wed Jun 15, 2022 2:47 pm

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

Postby obsrvr524 » Sat Jul 02, 2022 6:20 am

Magnus Anderson wrote:
Magnus Anderson wrote:..What's impossible in concept is also impossible in reality...
obsrvr524 wrote:That is not always true

"Impossible in concept" means "self-contradictory".

Being impossible in your concepts does not mean that reality obeys your conceptual conundrum.

Magnus Anderson wrote:Zeno's dichotomy paradox does not concern itself with straight lines.

It actually does.

Magnus Anderson wrote:I certainly don't see how Zeno's paradox shows that there are things that are impossible in concept but that there are nonetheless possible in reality.

It shows that since every motion requires traveling through halfway to the next step before you can get to the next step - the next step could never be reached - which means that no step could begin - which is not reality. Even when you imagine the smallest steps being a finite distance - how do you travel that first finite distance without passing halfway there first? If you say that step requires only the smallest duration of time - how did that handle the fact that you would have to get passed halfway in zero time?

Magnus Anderson wrote:the question is merely whether it's conceptually possible for motion to exist if space is infinitely divisible. If it's not, it follows that space isn't infinitely divisible.

That was one question. Then the question arose as to whether distances and durations add in the simple minded way as the Newton era. And that questions whether your conclusion that distances must be finite is valid. And it isn't.

Magnus Anderson wrote:
As it turns out - objects on that Plank level really do exist in multiple places at the same time
It says "You are here and not here". It's "P and not-P".

"It is here AND there" - is NOT "it is here and NOT here".

Magnus Anderson wrote:What I'm still missing is a clear definition of the word "clarity".

Then let me exchange that word in my post with "simple-minded". Reality does not behave in the simple-minded ("clear") way that you think.

The only thing that I'm getting is that you're saying that reality is best described using oxymorons.[/quote]
              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

Postby Magnus Anderson » Sat Jul 02, 2022 12:29 pm

obsrvr524 wrote:"It is here AND there" - is NOT "it is here and NOT here".


If "here" and "there" refer to two different locations, rather than one and the same location, then it follows that they are two different things i.e. that "there" is different from "here", which is to say, that "there" is not "here". Thus, what you're saying is "It is here AND not here". You're not being explicit about it, of course, but that's what you're implicitly stating. And that makes it a logical contradiction -- a blatant one.

Then let me exchange that word in my post with "simple-minded". Reality does not behave in the simple-minded ("clear") way that you think.


Your original claim was that "reality consists of vagueness skewed upon vagueness". I asked you to define the word "vagueness". You proceeded by claiming that the word "vagueness" means "lack of distinction" or "lack of clarity". I explained what these terms normally mean and I explained that they actually mean two different things (meaning that "vagueness" cannot be described by both -- only by one of them.) You ignored that and went on to say that I'm "presuming that clarity exists" and that "every location is a blur". I then, once again, asked you to define what you mean by "clarity" and now you're telling me that "clarity" means "simple-minded". Really? So what you're actually saying is that I'm presuming that simple-mindedness exists and that reality consists of lack of simple-mindness skewed upon lack of simple-mindness?

Your argument, in essence, is that reality cannot be described using meaningful and non-contradictory statements and that it can only be described using meaningless or self-contradictory statements such as "It is here and there at the same time".

Being impossible in your concepts does not mean that reality obeys your conceptual conundrum.


I understand and I agree that our beliefs are not necessarily true. What I'm saying is merely that, if a belief is self-contradictory, then it's necessarily false. "I am here and there" is an example of such a belief. Necessarily false because it's a contradiction in terms. "Time isn't made out of points in time" is another. These are contradictions in terms, i.e. impossible in concept, and because of that, they are necessarily false.

It shows that since every motion requires traveling through halfway to the next step before you can get to the next step - the next step could never be reached - which means that no step could begin - which is not reality.


Do you agree that it is impossible in concept to cross an infinitely divisible line?

Do you also agree that everything that is impossible in concept is also impossible in reality?

If you agree with both, it logically follows that crossing an infinitely divisible line is impossible in reality.

Do you also agree that motion is possible in reality and that it actually happens all the time?

If you agree with that too, it follows that space and time aren't infinitely divisible.

Even when you imagine the smallest steps being a finite distance - how do you travel that first finite distance without passing halfway there first? If you say that step requires only the smallest duration of time - how did that handle the fact that you would have to get passed halfway in zero time?


Because there is no halfway. There are no points between the first point and the immediately adjacent point. You can imagine them, of course, but again, we're not talking about what can be imagined.
Magnus Anderson
ILP Legend
 
Posts: 6117
Joined: Mon Mar 17, 2014 7:26 pm

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

Postby Motor Daddy » Sat Jul 02, 2022 2:29 pm

Magnus Anderson wrote:Do you agree that it is impossible in concept to cross an infinitely divisible line?

Do you also agree that everything that is impossible in concept is also impossible in reality?

If you agree with both, it logically follows that crossing an infinitely divisible line is impossible in reality.

Do you also agree that motion is possible in reality and that it actually happens all the time?

If you agree with that too, it follows that space and time aren't infinitely divisible.


Your logic is faulty.

1. A line is in fact infinitely divisible, meaning you can keep dividing by 2 infinitely and never get to 0.

1 divided by 2 = .5.
.5 divided by 2 = .25.
.25 divided by 2 = .125.
and on and on infinitely, and you never get to zero.

So the line is in fact infinitely divisible. That is a FACT!

2. It is a fact that there is motion from my house to Walmart, which is motion from point A to point B.

Those are both absolutely true facts, and it DOES NOT FOLLOW that "crossing an infinitely divisible line is impossible in reality" and "space and time aren't infinitely divisible." That is your failure in your logic.

Space is measured in distance, ie, 1.0 meter of distance from point A to point B. That space is in fact infinitely divisible using our system of math.

There is space (3 dimensional distance) which is volume, and there is math, which according to the concept of division can in fact divide a distance of 1.0 unit infinitely and never get to a distance of zero.

Again you mix up the concepts of addition and division!


A distance is not the sum of the addition of infinite parts, but distance can be divided infinitely.


Another of your logic failures is that you continuously think of "infinite" as a number of parts, or a sum of all parts, as if it were finite, which it is not.

Infinite simply means "continuous" meaning something continues with no end. It has nothing to do with a "sum" or "the total of all parts", it is the concept of never ending.
User avatar
Motor Daddy
Philosopher
 
Posts: 1693
Joined: Fri Aug 27, 2021 5:32 pm

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

Postby Magnus Anderson » Sat Jul 02, 2022 6:56 pm

Motor Daddy wrote:A line is in fact infinitely divisible, meaning you can keep dividing by 2 infinitely and never get to 0.


Sure, if you define the word "line" to be something that is infinitely divisible. But you don't have to define it that way.

2. It is a fact that there is motion from my house to Walmart, which is motion from point A to point B.


Everyone already agrees with that.

Those are both absolutely true facts, and it DOES NOT FOLLOW that "crossing an infinitely divisible line is impossible in reality" and "space and time aren't infinitely divisible." That is your failure in your logic.


You have a serious trouble following what other people are saying. You've been told this a number of times in the past. No progress has been made so far.

What I said is that IF he agrees that it is impossible in concept to cross an infinitely divisible line and IF he agrees that everything that is impossible in concept is also impossible in reality, that it necessarily follows that crossing an infinitely divisible line is also impossible in reality. You haven't addressed this argument at all.

Space is measured in distance, ie, 1.0 meter of distance from point A to point B. That space is in fact infinitely divisible using our system of math.


"Distance" merely means "the number of spatial points between two spatial points". Nothing else. But note that when I say "spatial point" I do not mean "zero width spatial point" but "the smallest region of space".

Although you can imagine that the number of spatial points between any two spatial points is infinite, and therefore infinitely divisible, whether any given portion of space is infinitely divisible or not has nothing to do with that -- it has nothing to do with what can be imagined.

A distance is not the sum of the addition of infinite parts, but distance can be divided infinitely.


If you can divide something infinitely, it means that that something is made out of an infinite number of parts, and thus, that it is the result of an addition of an infinite number of parts. It's basic logic.

Another of your logic failures is that you continuously think of "infinite" as a number of parts, or a sum of all parts, as if it were finite, which it is not.


We've been over this. "An infinite queue of people" is saying that the number of people in that queue is larger than every integer. It's specifying the quantity of the people in that queue AND NOTHING ELSE. You can play word games all you want by saying "Nah, that's not how the word number is defined" but the point is that the concept of infinity is far more closer in its constitution to the concept of natural number than many numerical concepts that you are fine categorizing as numbers e.g. "1/2" which means "half". All this talk about how infinity is not a number is utter non-sense.
Magnus Anderson
ILP Legend
 
Posts: 6117
Joined: Mon Mar 17, 2014 7:26 pm

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

Postby Motor Daddy » Sat Jul 02, 2022 7:37 pm

Magnus Anderson wrote:If you can divide something infinitely, it means that that something is made out of an infinite number of parts, and thus, that it is the result of an addition of an infinite number of parts. It's basic logic.


There you are again, your massive confusion on addition and division.


"Dividing something infinitely" means there is no number of parts. The very reason you can divide it infinitely is that it never reaches a point which the part being divided by 2 is equal to zero, hence you never finish dividing, hence you divide continuously, infinitely, forever, and never reach zero. You NEVER completely divided 1.0 into a number of parts that when added together is the sum 1.0.

No matter how many times you keep dividing by 2, the parts will never equal zero, so the division is infinite, meaning there is no end to the division. The fact that the division does not end means there is no finite number of parts that add up to the whole. You can deny that all you want to but that is just your denial to the REALITY.

The reality is:

1 divided by 2 = .5
.5 divided by 2 = .25
.25 divided by 2 = .125
.125 divided by 2 = .0625

and you can continue that INFINTELY and never get to a point where the division by 2 will equal 0. That means there is no finite number of parts that can be added up to be 1.0.
So your BS that the sum of the parts is 1.0 is just that, a load of BS!
User avatar
Motor Daddy
Philosopher
 
Posts: 1693
Joined: Fri Aug 27, 2021 5:32 pm

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

Postby obsrvr524 » Sat Jul 02, 2022 9:18 pm

Magnus Anderson wrote:Your argument, in essence, is that reality cannot be described using meaningful and non-contradictory statements and that it can only be described using meaningless or self-contradictory statements such as "It is here and there at the same time".
---
I understand and I agree that our beliefs are not necessarily true. What I'm saying is merely that, if a belief is self-contradictory, then it's necessarily false.

That is not my argument. You are again assuming that your "logic" is the only option - which happens to be a false assumption in this case. Let me try to give an example - again -

When you add 0.75 of something to 0.75 of something, you expect to get 1.5 of that something, right? It is logical and necessarily true. Or is it?

When Newton added 0.75v to 0.75v he got 1.5v and everyone was impressed with his understanding of irrefutable laws of motion. He was right -- well unless v happened to be in the vicinity of c the speed of light.

When v became c -- suddenly commonly understood logic no longer fit reality. 0.75c + 0.75c does not equal 1.5c and we know that for a fact. So what happened?

Physical reality was not following commonly understood logic - so after many years of arguing about it - eventually most people came to understand a new common logic - that velocities in reality do not simply add. They add - just not in that simple-minded clear and easy way Newton thought.

I'm sure you already knew that much (I hope).

Years after that revelation changed what was common logical understanding (common ontology) - quantum mechanics ran into a similar issue with smallness - things didn't seem to simply add or subtract down on an extremely small scale. Again - simple-minded common ontological understanding was common up short.

Physical reality was showing yet another false assumption being made by people - simple true-false logic wasn't working.

From that revelation they have put together quantum physics - with all kinds of ontological changes from what was common logical and necessary understanding. Part of that new understanding (for some - they argue a lot) is that there is a minimum length for reality itself - Plank length. And that implies a minimal size and also a minimal duration.

In both cases of velocities not adding in a simple-minded way and also small sizes not adding in a simple-minded way - new theories arose - and those theories were eventually shown to be too simple minded as well.

Relativity doesn't always work. Quantum Physics doesn't always work. And that tells you that whatever your understanding of what is logically true or not - is flawed in some way. It doesn't mean that it can't be understood - eventually. It means that right now assumptions are being made that are in error.

My "argument" is about one of the assumptions being made that is strangely false - leading to what could be called a "smear" of existence where what exists and doesn't and where it exists and doesn't is not a "black-white", "here-there" reality. On the Plank level - locations and durations are NOT binary choices.

Your assumption that if something is here then it is necessarily not there - is a logic that happens to not be true on Plank level reality. There are logical reasons why it must be that way. Logic demands that it actually can't be any other way.

On the Plank level things always exist at multiple points at the same time.

That doesn't fit your logic for the same reason that 0.75v + 0.75v doesn't make 1.5v -- when v is close to c. You are behind the times.



Also you seem to be conflating set theory with physical reality -- they don't 100% mix.
              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

Postby Magnus Anderson » Sat Jul 02, 2022 9:48 pm

Motor Daddy wrote:"Dividing something infinitely" means there is no number of parts.


That which has no parts does not exist. It's nothing.

That which does not have more than one part cannot be divided -- it's indivisible.

That which has \(x\) number of parts where \(x\) is an integer greater than \(0\) can be divided but not infinitely.

Only that which has an infinite number of parts can be divided infinitely.

You NEVER completely divided 1.0 into a number of parts that when added together is the sum 1.0.


"1" divided by "infinity" is equal to "infinitesimal". In other words, "1" is made out of an infinite number of infinitesimals.

1 / infinity = infinitesimal

infinity x infinitesimal = 1

infinitesimal + infinitesimal + infinitesimal + ... = 1

A person standing in an infinite queue of people is an infinitesimal compared to the infinite queue itself. The infinite queue itself, in turn, is infinity compared to every person standing in it.
Magnus Anderson
ILP Legend
 
Posts: 6117
Joined: Mon Mar 17, 2014 7:26 pm

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

Postby Magnus Anderson » Sat Jul 02, 2022 10:12 pm

obsrvr524 wrote:Physical reality was showing yet another false assumption being made by people - simple true-false logic wasn't working.


That's what happens when people spend a lot more time on empirical research than they do on conceptual analysis. They end up thinking that there are things in reality that can be represented using non-sensical, self-contradictory, terms. Figuratively speaking, they end up thinking that square-circles exist and that the earlier conviction, that they do not, is simple-minded and behind the times (when, in reality, they lost common-sense.)

Your assumption that if something is here then it is necessarily not there - is a logic that happens to not be true on Plank level reality.


No amount of physics can refute the obvious observation that the word "here" and the word "there" are defined as opposite to each other.

It's similar to how no amount of time spent on searching for square-circles can ever result in you finding one simply because the term "square-circles" is a meaningless term.

What can happen instead is for people to be deceived as a consequence of not spending enough time examining concepts.

There are logical reasons why it must be that way. Logic demands that it actually can't be any other way.


Really? Logic demands logical contradictions? Logic demands P and not-P?

You are behind the times.


And you fell into the trap of postmodernism. You are a step closer to becoming a liberal. "Gender isn't binary because there are no binaries in reality."
Magnus Anderson
ILP Legend
 
Posts: 6117
Joined: Mon Mar 17, 2014 7:26 pm

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

Postby Motor Daddy » Sat Jul 02, 2022 10:19 pm

Magnus Anderson wrote:That which does not have more than one part cannot be divided -- it's indivisible.


So you are claiming that 1 pizza can't be divided, that it is indivisible?

I remind you, 1.0 whole pizza is 1.0 part. It is 1 whole area. If the diameter of the pizza is 14", then the WHOLE area (1 area) is 3.14159(7x7), or the area is 153.93791 square inches of area.

That is the area of 1 whole part of pizza, which is 1.0 pizza.

When you divide the pizza into 2 equal parts with a pizza cutter, then you have 2 parts, each is .5 pizza.

A pizza is 1.0 pizza, not an infinite number of parts added together. You can divide the pizza infinitely, but there is NO SUCH THING as a pizza made of infinite parts of zero area! That is NONSENSE!

If you claim the parts have an area greater than zero, then what you are claiming is that there is a FINITE number of parts that add up to 1.0 whole pizza.

So to clear up your confusion, parts of area greater than zero have a finite number of parts that make up 1.0 whole pizza. Parts of ZERO area means there is no pizza.
If the parts are zero it doesn't matter how many parts you have, there is ZERO pizza!
If the parts are greater than zero then there is a limit to the number of parts that make up 1.0 pizza, which means there is NOT infinite parts. More parts would mean a greater than 1.0 pizza, which again is total BS!
User avatar
Motor Daddy
Philosopher
 
Posts: 1693
Joined: Fri Aug 27, 2021 5:32 pm

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

Postby Magnus Anderson » Sat Jul 02, 2022 10:57 pm

Motor Daddy wrote:So you are claiming that 1 pizza can't be divided, that it is indivisible?


No. Pizza isn't indivisible. I am talking about things that are made out of no more than 1 part. Pizza is obviously made out of many parts.

I remind you, 1.0 whole pizza is 1.0 part.


Yes but pizza is obviously made out of more than 1 part. That's why you can cut it into lots and lots of pieces.

You're using the word "part" to refer to the entire pizza. You can also use it to refer to its halves. In that case, pizza would be made out of 2 parts.

What I said is that if a thing is made out of no more than one part, it can't be divided. Pizza is obviously made out of more than 1 part.

A pizza is 1.0 pizza, not an infinite number of parts added together.


If it's infinitely divisible, it's made out of an infinite number of parts added together.

You can divide the pizza infinitely, but there is NO SUCH THING as a pizza made of infinite parts of zero area! That is NONSENSE!


What's non-sensical is your claim that a thing that is NOT made out of an infinite number of parts can be divided into an infinite number of parts. That is truly non-sensical.

If you claim the parts have an area greater than zero, then what you are claiming is that there is a FINITE number of parts that add up to 1.0 whole pizza.


Not at all. Think of an infinite queue of boxes where each box has non-zero size. Let's say that each box is 1 meter long. They are placed in line, next to each other, with no space in between. The infinite queue, then, is an infinite number of meters long. And if we use the word "queue" to refer to the length of that queue, then it's length can also be expressed as "1 queue". So it's length is both "1 queue" and "infinity meters". How is that possible? How is it possible to use "1" and "infinity" to refer to the same exact length? The answer is . . . units.
Magnus Anderson
ILP Legend
 
Posts: 6117
Joined: Mon Mar 17, 2014 7:26 pm

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

Postby Motor Daddy » Sat Jul 02, 2022 11:05 pm

Magnus Anderson wrote:You're using the word "part" to refer to the entire pizza. You can also use it to refer to its halves. In that case, pizza would be made out of 2 parts.


Exactly my point! The 2 parts are each .5 (1/2) of 1.0 whole pizza. And cut it into 4 parts and the parts are each 1/4 pizza. Cut it into 8 parts and each part is 1/8 pizza.

..
..
..
Cut it into 10 million parts and each part is 1/10,000,000
Cut it into 500 Trillion parts and each part is 1/500,000,000,000,000

You see? Each part is 1 of that many parts.

So to have parts you need to have a QUANTITY OF PARTS, which is a NUMBER OF PARTS!

There is no such thing as cutting a pizza into Infinity parts, each of those parts being 1/infinity, that is total BULLSHIT!
Last edited by Motor Daddy on Sun Jul 03, 2022 4:53 am, edited 1 time in total.
User avatar
Motor Daddy
Philosopher
 
Posts: 1693
Joined: Fri Aug 27, 2021 5:32 pm

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

Postby Magnus Anderson » Sat Jul 02, 2022 11:40 pm

Motor Daddy wrote:There is no such thing as cutting a pizza into Infinity parts, each of those parts being 1/infinity, that is total BULLSHIT!


It depends on how you're cutting it. If you're cutting it into 2 halves and then each half into 2 halves and then each half into 2 halves and so on, you will never end up with individual parts. In effect, you're committing the very same mistake you're accusing Zeno of.

Infinity / 2 = Half of infinity
Half of infinity / 2 = Quarter of infinity
Quarter of infinity / 2 = Eighth of infinity
Etc.

Another way to demonstrate my point:

Take the set of natural numbers that is {1, 2, 3, ...}. Divide it infinitely by splitting it into 2 halves at each step. What do you get?

DIVISION #1
{1, 3, 5, ...}
{2, 4, 6, ...}

DIVISION #2
{1, 5, 9, ...}
{3, 7, 11, ...}
{2, 6, 10, ...}
{4, 8, 12, ...}

etc

There is no end to this process. There is no point at which you'll have an infinite number of singleton sets. And yet, individual elements exist.
Magnus Anderson
ILP Legend
 
Posts: 6117
Joined: Mon Mar 17, 2014 7:26 pm

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

Postby origami » Sat Jul 02, 2022 11:57 pm

Right, but you're still dividing an infinite set. The addition of all numbers in the set will always be an infinite quantity.

But 5 minutes is not an infinite quantity.

You have granted that your theoretical minimum points must have quantity.

If they are any quantity, any portion of 5 minutes, then the division example you gave will eventually reduce the elements in the set to 1.

For example,

{1,2,3,4,5,6,7,8}

{1,3,5,7}
{2,4,6,8}

{1,5}
{3,7}
{2,6}
{4,8}

{1}
{5}
{3}
{7}
{2}
{6}
{4}
{8}
There's no one thing that's true. It's all true.
Ernest Hemingway
User avatar
origami
Philosopher
 
Posts: 2313
Joined: Wed Jun 15, 2022 2:47 pm

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

Postby Magnus Anderson » Sun Jul 03, 2022 12:05 am

origami wrote:Right, but you're still dividing an infinite set. The addition of all numbers in the set will always be an infinite quantity.

But 5 minutes is not an infinite quantity.


Well, my point all along has been that, if something is infinitely divisible, that it is necessarily composed of an infinite number of parts. In other words, if something is made out of less than an infinite number of parts, it cannot be infinitely divided.

You have granted that your theoretical minimum points must have quantity.


Yes, they are not zero.

If they are any quantity, any portion of 5 minutes, then the division example you gave will eventually reduce the elements in the set to 1.


If "5 minutes" is composed of less than an infinite number of parts, then you're right. But again, if "5 minutes" is infinitely divisible, it is necessarily composed of an infinite number of parts. It cannot be any other way.
Magnus Anderson
ILP Legend
 
Posts: 6117
Joined: Mon Mar 17, 2014 7:26 pm

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

Postby origami » Sun Jul 03, 2022 12:29 am

Right, but if these minimum parts have quantity, an addition process will eventually bring that quantity up to 5 minutes.
There's no one thing that's true. It's all true.
Ernest Hemingway
User avatar
origami
Philosopher
 
Posts: 2313
Joined: Wed Jun 15, 2022 2:47 pm

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

Postby origami » Sun Jul 03, 2022 12:29 am

If 5 minutes is infinitely divisible, it only means that there is no minimum point.
There's no one thing that's true. It's all true.
Ernest Hemingway
User avatar
origami
Philosopher
 
Posts: 2313
Joined: Wed Jun 15, 2022 2:47 pm

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

Postby obsrvr524 » Sun Jul 03, 2022 1:59 am

Magnus Anderson wrote:No amount of physics can refute the obvious observation that the word "here" and the word "there" are defined as opposite to each other.

They are actually not.

So you believe that 0.75v + 0.75v = 1.5v?

Magnus Anderson wrote:Logic demands P and not-P?

I never said anything about "not-P" -- that is Your assumption.

Magnus Anderson wrote:"Gender isn't binary because there are no binaries in reality."

:lol:
They are just playing a word game. THEY define "gender" as the way a person behaves -- not their chromosome makeup. So to them - they are not lying. But it certainly is postmodern propaganda for their globalist goals.

Magnus Anderson wrote:That which has no parts does not exist. It's nothing.

And unless you are also playing word games - that statement is patently false.

How do you define a "part"? Is it any different than a portion?
              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

Postby Magnus Anderson » Sun Jul 03, 2022 11:07 am

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.

On the other hand, you did not merely say that "Objects on the Plank level exist here and there at the same time" you also said "Objects on the Plank level exist at multiple places at the same time". You obviously agree that the two statements mean the same thing. So, if you're redefining words, you're not merely redefining the word "there", you are also redefining the word "multiple".

You are either redefining words (in which case you might not be contradicting yourself) or you are not (in which case you are contradicting yourself.) Which one is the case?

And if you are redefining words, why should I care?

I never said anything about "not-P" -- that is Your assumption.


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.

They are just playing a word game. THEY define "gender" as the way a person behaves -- not their chromosome makeup. So to them - they are not lying. But it certainly is postmodern propaganda for their globalist goals.


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

And unless you are also playing word games - that statement is patently false.

How do you define a "part"? Is it any different than a portion?


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. 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. A thing composed of more than one thing has more than one part and is a divisible thing. A thing composed of an infinite number of things has an infinite number of parts and it's an infinitely divisible thing.
Magnus Anderson
ILP Legend
 
Posts: 6117
Joined: Mon Mar 17, 2014 7:26 pm

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

Postby Magnus Anderson » Sun Jul 03, 2022 11:29 am

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.

Consider that the statement "A collection made out of two collections that are made out of two collections and so on ad infinitum" can be used to represent any collection. An empty set, for example, can be described using it, because an empty set can be said to consist of two subsets consisting of two subsets consisting of two subsets and so on. In the case of the empty set, all of these subsets would be empty. But the statement can also be used to describe non-empty sets e.g. {1, 2, 3}. That set could be said to consist of a subset that is {1, 2} and a subset that is {3}. Then, you could say that the subset that is {1, 2} consists of {1} and {3}, and the subset that is {3} consists of {3} and {}. Then you could say that {1} consists of {1} and {}, {3} of {3} and {}, {3} of {3} and {}, and {} of {} and {}. The process can be continued infinitely. What this means is that the above statement is all-encompassing and not particularly informative. If you then add to that statement that there are no elements, you end up with a statement that can only describe empty sets. In other words, you end up with . . . nothing at all. An empty set is nothing at all.

In order for "5 minutes" to be something rather than nothing, it must be composed of something. You can't just say it's a collection made out of collections that are made out of collections that are made out of collections and so on. That tells us nothing about what "5 minutes" is. And if you add that there are no "minimum points", you're saying it's nothing at all.
Magnus Anderson
ILP Legend
 
Posts: 6117
Joined: Mon Mar 17, 2014 7:26 pm

PreviousNext

Return to Science, Technology, and Math



Who is online

Users browsing this forum: No registered users