If there is an infinite amount of numbers between 0 and 1, how is either ever achieved? To illustrate this better, .9 becomes .99 and then .999 and so on. Never reaching 1. And same with zero. .1 to .01 and then .001 and so on. Some of you may know this as dichotomy paradox but please I'd like to hear from some of you on this.
you add 0.1 to 0.9 and VOILA !
sup Zeno
Numbers are abstractions.
Now, if you were interested in a physical version of this, like Zeno's Arrow? The universe has a defined "resolution"- the smallest amount of space an object can take up.
>>7978628
Not so fast buster. Let's say you want to drive up to 1mph. How can you achieve that if .999 continues forever? Likewise if you want to slow down to 0 mph
>>7978616
Let's say you're walking from 0 to 1 at a constant rate, say k. Then the time taken to walk is .9/k+.09/k+... =(.9 + .09 +...)/k =1/k units of time. Wow. Much finite. Stop being retarded.
>>7978631
You are speaking of Planck length. However that's only a theory thus far. Also, i refuse to believe the universe has a finite limit to how small it can get.
>>7978644
So you refuse to believe in a solution to a paradox because...?
>>7978635
Stop being an incompetent fuck for a sec. Obviously I know certain mathematics solves the issue. But we aren't concerned with that, we are talking about how those mathematics contrast with a fluid visualization of an object in motion. The numbers infinitely increasing or decreasing as a decimal.
>>7978654
It's a theory, not a solution. I will believe fact however.... Is that so strange?
>>7978644
Yeah I believed there was a limit to how small things can get, then I saw your penis.
>>7978616
>achieved?
By definition. 1 is the basis of all numbers and zero is the origin of all numbers. Think vector space.
>>7978616
>Never reaching 1.
It reaches one at the exact moment you iterate to infinity. The equivalent lower bound isn't actually .1 but 0.000...
>>7978633
How can you have wheels of finite perimeter if pi is infinite?
>>7978675
That seems like a matter of perspective. The dilemma here is this:
Humans stated using mathematics that numbers are infinite.
But at the same time, created measuring devices that are precise to a certain digit. Any number after is negligible. Like a speedometer etc.
This is how we have our paradox.
>>7978616
>achieved
What do you mean by this?
Every natural number can easily be constructed inductively from the Peano Axioms.
>>7978704
Read up on dichotomy paradox and have your mind blown.
>>7978631
This isn't true - there is a limit to the point where you can say two things occupy a space but this doesn't mean that the universe is 'quantised '
>>7978709
*occupy a different space
>>7978707
There is no paradox though. Zeno's understanding of the real numbers is backwards.
>>7978692
Doing two things at once isn't a paradox.
>>7978716
Or are they? Do you truly know that?
There are many ways to slice the same pie. The biggest barrier for the human being is his arrogance derived from something we like to call logic. The ironic thing about logic is that it's not actually logical to approach everything expecting the same set of rules.
>>7978728
I just realizing the all cognition exists in a state of basic decay, and the desire to communicate is the only force in the universe the keeps us sane. Your argument literally has no reason to exist, since it's functionally equivalent to the effects of total isolation.
>>7978740
every comment you make is absolute garbage littering the fucking board
at least you make it easy to spot it as soon as the name
Everything is relative to something else. Did you guys forget Einstein already?
If you are talking about space... can you divide the space into infinite pieces? Can you divide an atom into infinite? can you take a proton and divide it forever into small pieces? That's the reason in the ancient Greek said that there must be a piece that you can not divide... and they called it an "atom" ( the prefix "a" means "not" and the word "tomos" means cut)
thus, where are not sure If we can keep dividing our atom into infinite pieces. therefore, If we can divide matter for ever, 0 to 1 will have an infinite measurable scale, otherwise it will stop at a certain point.
>>7978746
You haven't read every comment I've made. Filter me if you don't like the subset of my posts you've been willing to read so far. Shitposting won't make me leave and it doesn't sound like you'll be in the mood for constructive criticism any time in the next week.
>>7978616
Egad!!! the solution to Zeno's paradox!!!!
https://www.youtube.com/watch?v=OORsz2d1H7s
>>7978776
note that at 0:36, the limit is destroyed and this unsung genius achieves walking through a door.
Seriously though, the nature of space is probably quantized
>>7978656
Our visualization is wrong, you silly goose. Motion isn't fluid.
>>7978769
Hey faggot, I'm not that guy, but I agree with him. From what I've seen, you lower the quality of this board and simply make it clear by taking on that stupid name. You generally lack sufficient rigor or understanding of topics to not sound like an idiot.
I'm pretty sure everyone realizes it. Don't blame that anon for saying it.
>>7978897
>Don't blame that anon for saying it.
I'm not. I'm just saying that it's a far cry from the kind of constructive criticism I'd need if people did want me to change my behavior. I realize not all of my posts are gold letter quality, but often times I write decent posts and get decent replies. There's not really anything for me to change on my end unless people want to get specific and critical. If you don't like the majority of my posts, just filter me. I don't think it's really a problem. I also don't think I really degrade the quality of the board much if at all.
>>7978910
>There's not really anything for me to change on my end unless people want to get specific and critical.
Attaching a name to yourself serves no purpose other than to get you cheap attention by making autists like >>7978746 buttmad.
Regardless of the quality of your posts you'd be a better user if you dropped the snowflake namefagging and remained anonymous.
>>7978616
Let me explain OP.
We construct the natural numbers and then the integers first. Then the rationals from those. So it's kind of out of order to say that 0.9 exists if 0 and 1 don't already exist in our system. In other words, we have the integers and then we define these decimals as existing between them. Not the other way around.
>how can 2 numbers have an infinite set of numbers between them?
That's what you're asking right?
What you're really asking is "why are rational numbers dense in the reals?"
For that, google a proof.
Here is one right here: http://math.stackexchange.com/questions/103839/proof-that-mathbbq-is-dense-in-mathbbr
Keep in mind that we define these things straight down to axioms and that your question is a merely a RESULT of these definitions which can be proven. It is a property, abstractly, which we observe. Thus to question "how can this be possible" is to question the definitions (of rational and real numbers) themselves. And that leads to a whole other set of questions. For now, at least, these are the best definitions we have and this is merely an important property of them.
Does this answer OPs question?
>>7978924
I'm aware of that. Dropping the name would help in certain ways but it'd also hurt in certain ways. The purpose is a bit abstract but since that purpose is the reason I post here in the first place, there's not much I can do about it even if I want to. I just have to deal with the occasional flame and let them filter me if they want. So far it hasn't been so bad, but if the rate of hate accelerates then I might have to reconsider my approach.
Also this is a bait thread, so I guess I could've skipped posting here if it's really bothering people that much.
>>7978974
I don't understand why you have to be such a showy faggot and take a trip in the first place.
>>7978692
No, that's not the paradox, Zeno stated the problem far more eloquently. The issue is that, if you assume it takes an infinite number of steps, each of which can be said to have a finite length, to reach a finite distance in a finite time, then what could possibly said to be the final step? This is how Zeno argues that our perception of continuous motion can't be entirely real, and it is a paradox worth taking seriously.
Mathematical reductions don't actually solve anything here.
>>7979112
Because AI researchers haven taken advantage of fear for long enough. I'm literally only here to provide a baseline for AI that will later be seeded with /sci/ content. My name is liable to be one of the few tangible types of metadata that AI will have available for forming a notion of identity. Basically I get more utility out of changing the way AI learn than I do from trying to get everyone that's afraid of AI to understand the concept of not having an identity.
>>7979137
>what could possibly said to be the final step?
I don't get it. What makes the final step more or less relevant than the first step, or the nth step? Isn't this just the same as asking how to index/order infinite sets?
>>7979217
>What makes the final step more or less relevant than the first step, or the nth step?
I don't get how you don't get this. If the steps are ordered so that the next step is always half the size of the previous, then there will always be another, smaller step that you have to travel through.
>Isn't this just the same as asking how to index/order infinite sets?
No.
>>7979221
Oh. Well there is no last step; there are infinitely many. That's kind of how infinity works. Asking if infinity has an end defies the definition of infinity.
Shame on all of you for taking the shit quality bait of a fourteen year old who thinks he's a philosopher
>>7978631
That's not how the Planck length works.
I mean, you can read the Wikipedia page and see that it says it has no confirmed physical significance.
>>7979226
>Asking if infinity has an end defies the definition of infinity.
But that's not what is being asked. The question is whether our own intuitive perception of reality ultimately makes physical sense, assuming motion is actually continuous.
Lets say that, for each 'step', the color of the ground underneath the walker is either red or blue, and this changes each step. The ground starts off blue. At the end of it all, when the walker has reached their destination, what color is the ground?
>>7978769
You always post stupid pretentious garbage. You spew bullshit and buzzwords all over this forum and don't understand the most trivial concepts when they are explained multiple times. In addition to contributing nothing because of your ignorance you posture and argue with people who are actually informed. Lose the trip and stop being a faggot or gtfo.
>>7978665
>>7979184
You're pretty insane tbqhwyfam. I have my bachelors in maths and computer science with specialization in cognitive sciences and psychology. Currently in grad school. Everything you just said is bullshit.
>>7979226
Let's say you want to walk from x=0 to x=1 with a continuous motion.
The end here is x=1.
But first you have to go to 0.5.
Then 0.75.
Then 0.9.
Then 0.99.
Then 0.999.
Then 0.999...
Then...
It's obvious that you CAN walk 1 meter, or 1 km, or whatever, but first you have to take infinitely many steps. So the question is how is there an end to a sequence of infinitely many steps?
