/sci/ - Science & Math » Thread #12431247

64KiB, 645x729, meirl.jpg

View Same Google iqdb SauceNAO

Anonymous Mon 07 Dec 19:59:36 2020 No.12431247 View Reply Original Report

Quoted By: >>12431269 >>12431302 >>12431316 >>12431330 >>12431342 >>12432697 >>12433260 >>12433273 >>12433324 >>12433362 >>12435092 >>12435521 >>12435528 >>12435924 >>12435943 >>12436082 >>12436767 >>12437767

brainlet here. can someone explain to me what gets around zeno's paradoxes?

Anonymous

Anonymous Mon 07 Dec 2020 20:04:17 No.12431269 Report

Quoted By: >>12435830

>>12431247
1/inf=0

Anonymous

Anonymous Mon 07 Dec 2020 20:08:02 No.12431281 Report

Quoted By:

convergence

Anonymous

Anonymous Mon 07 Dec 2020 20:15:21 No.12431302 Report

Quoted By:

>>12431247
The turtle is slower than you think.

Anonymous

Anonymous Mon 07 Dec 2020 20:18:12 No.12431316 Report

Quoted By: >>12433612 >>12437901

>>12431247
Nothing gets around zenos paradox. Reality just doesn't have many zeno paradoxes.

If I say, you walk 1 meter in 1 second, then half a meter in 1 second, then half of a half in one second, then after an infinite amount of time you'll have moved 2 meters total.

But in reality you aren't limited to this decrease in speed

Anonymous

Anonymous Mon 07 Dec 2020 20:21:43 No.12431330 Report

Quoted By:

>>12431247
Zeno converges to a small enough degree that it reaches the quantum level where eventually Zeno can access a point below 0 because of you know quantum mechanical stuff

Anonymous

Anonymous Mon 07 Dec 2020 20:25:55 No.12431342 Report

Quoted By: >>12431350

>>12431247
Space is not infinitesmal; i.e. there is a finite pixellation of space.

Anonymous

Anonymous Mon 07 Dec 2020 20:27:15 No.12431350 Report

Quoted By: >>12431352 >>12435547

>>12431342
imagine being so confident in spreading misinformation

Anonymous

Anonymous Mon 07 Dec 2020 20:28:31 No.12431352 Report

Quoted By: >>12431357

>>12431350
Imagine being a nigger, nigger

Anonymous

Anonymous Mon 07 Dec 2020 20:30:14 No.12431357 Report

Quoted By: >>12431523

>>12431352
wrong, and you're also a retard. space is commonly agreed to be continuous, only untestable fringe theories state otherwise

Anonymous

Anonymous Mon 07 Dec 2020 21:13:13 No.12431523 Report

Quoted By: >>12431941

>>12431357
The burden of proof is on continuous space, what proof is there?

Anonymous

Anonymous Mon 07 Dec 2020 22:53:15 No.12431941 Report

Quoted By: >>12432728 >>12433247

>>12431523
??????????????????
you can't just arbitrarily decide where the burden of proof lies. ALL of our current theories only work with continuous spacetime. there is not ONE theory that is testable and supports discrete safetime, therefore the burden of proof is on you retard.
I refuse to believe you're this dumb.

Anonymous

Anonymous Tue 08 Dec 2020 02:11:35 No.12432697 Report

Quoted By:

>>12431247
As any other beta would do to disprove a theorem. Simply provide a counter example.

Anonymous

Anonymous Tue 08 Dec 2020 02:23:42 No.12432728 Report

Quoted By: >>12433232

>>12431941
>ALL of our current theories only work with continuous spacetime
That's simply because they're too lazy to work out what happens in the discrete case. Continuous analysis is just the degenerate version of discrete analysis.
Every physical theory that we have could just as well be formulated without resorting to the "real numbers" and give equal predictions. It would probably look way more messy though and contain many asterices, which is why people don't want to do it.
The laziness and refusal of physicists and mathematicians to look at their theories and eliminating all but the most crucial assumptions is not proof that the assumptions they do make are valid or have evidence for.

Anonymous

Anonymous Tue 08 Dec 2020 05:17:26 No.12433232 Report

Quoted By:

>>12432728
>they're too lazy
projection, the post

Anonymous

Anonymous Tue 08 Dec 2020 05:22:55 No.12433247 Report

Quoted By: >>12433255

>>12431941
>ALL of our current theories only work with continuous spacetime

and in practice ALL of our current theories have an accepted rate of measurement error that could just as easily be explained by space being quantized at some level. Rather than just saying "everything is continuous because I say so" like a retard why not just accept that both are possible?

Anonymous

Anonymous Tue 08 Dec 2020 05:24:04 No.12433255 Report

Quoted By: >>12433366

>>12433247
>and in practice ALL of our current theories have an accepted rate of measurement error that could just as easily be explained by space being quantized at some level. Rather than just saying "everything is continuous because I say so" like a retard why not just accept that both are possible?

Whole numbers do not exist. Only ratios. There is no paradox here. And yes, Universe is continuous.

Anonymous

Anonymous Tue 08 Dec 2020 05:24:52 No.12433260 Report

Quoted By:

>>12431247
A pair of socks

Anonymous

Anonymous Tue 08 Dec 2020 05:27:13 No.12433273 Report

Quoted By:

>>12431247
Continuity vs quantization. If the distance between Zeno and the finish line is continuous, you can divide it infinitely forever. But if it's quantized, then at some point Zeno will have to cross the finish line as he reaches the last quanta of distance, and passes it

Anonymous

Anonymous Tue 08 Dec 2020 05:41:56 No.12433324 Report

Quoted By: >>12433327 >>12435113 >>12435153 >>12436852

>>12431247
god, so many brainlets above
$\sum_{n=0}^\infty \frac{1}{2^n} = \lim_{x\to\infty} \frac{1}{2}\frac{1-(1/2)^n}{1-1/2} = 1$
simple as

Anonymous

Anonymous Tue 08 Dec 2020 05:43:01 No.12433327 Report

Quoted By:

>>12433324
*made a typo. Obviously n goes to infinity, not x.

Anonymous

Anonymous Tue 08 Dec 2020 05:45:35 No.12433336 Report

Quoted By: >>12433343

Why do so many retards think convergence solves the paradox?

Anonymous

Anonymous Tue 08 Dec 2020 05:48:14 No.12433343 Report

Quoted By:

>>12433336
because it does, you mong

Anonymous

Anonymous Tue 08 Dec 2020 06:01:13 No.12433362 Report

Quoted By:

>>12431247
Have you ever tried racing a turtle? They're slow as shit unless you take a nap halfway through.

Anonymous

Anonymous Tue 08 Dec 2020 06:02:02 No.12433366 Report

Quoted By: >>12433407

>>12433255
>Whole numbers do not exist. Only ratios

1/1 is a ratio dumbfuck, what the fuck are you even on about

Anonymous

Anonymous Tue 08 Dec 2020 06:16:50 No.12433407 Report

Quoted By: >>12433461 >>12433632

>>12433366
>1/1 is a ratio dumbfuck, what the fuck are you even on about

To understand Zenos Paradox you must understand that all is relative. All is ratio. Even time itself is simply a ratio.

How long does it take the turtle to cross the path? Half the rotation of the Earth.

The Turtle cannot be measured in isolation because the Turtle is not in isolation. The Turtle is relative.

Anonymous

Anonymous Tue 08 Dec 2020 06:40:26 No.12433461 Report

Quoted By: >>12433500

>>12433407
what strain are you on? I want to try some.

Anonymous

Anonymous Tue 08 Dec 2020 06:56:52 No.12433500 Report

Quoted By:

>>12433461
>what strain are you on?

Optimum Theory

Anonymous

Anonymous Tue 08 Dec 2020 07:41:05 No.12433612 Report

Quoted By:

>>12431316
Or when you walk 2m, it's just 2m. You can represent it as 1m in 1s then 1/2 m in 1/2 s etc to infinity but it's still just a 2.

Anonymous

Anonymous Tue 08 Dec 2020 07:47:34 No.12433632 Report

Quoted By:

>>12433407
>To understand Zenos Paradox you must understand that all is relative. All is ratio. Even time itself is simply a ratio.
>How long does it take the turtle to cross the path? Half the rotation of the Earth.
>The Turtle cannot be measured in isolation because the Turtle is not in isolation. The Turtle is relative.

In addition to this. Time is not "real". Time is derivative. When asking "how much time does it take?" You are really asking, "how many rotation(s) of an Earth does it take?" Which in turn can only be understand relative to something else. Optimum shit

Anonymous

Anonymous Tue 08 Dec 2020 16:49:41 No.12435092 Report

Quoted By:

>>12431247
it's bullshit
like say the distance of your hands is 2 meters, and you're trying to clap, you're not actually halving it until it reaches 0
clapping is simply reducing the distance until it reaches 0
so instead of 2, 1, 1/2, 1/4, 1/8, 1/16, 1/32 ... 0
it's actually 2, 1.9, 1.8, 1.7, ... 0

Anonymous

Anonymous Tue 08 Dec 2020 16:53:11 No.12435113 Report

Quoted By: >>12435139

>>12433324
Do you realize the only thing you've said with this is that Achiles get arbitrarily close to the tortoise, which was never disputed in the first place.
You haven't solved shit.

Anonymous

Anonymous Tue 08 Dec 2020 16:58:37 No.12435139 Report

Quoted By: >>12435142 >>12435391 >>12436852

>>12435113
no, I said that despite having infinitely many steps, they can occur in a finite time and over finite space. I don't get why this is such a big deal. You certainly can do infinitely many operations over a bounded interval. Hell, you can do them over an instantaneous moment in time. For example you can just do nothing infinitely many times (literally identity operation of a group).

Anonymous

Anonymous Tue 08 Dec 2020 17:00:01 No.12435142 Report

Quoted By: >>12435153

>>12435139
>You certainly can do infinitely many operations over a bounded interval
How?
>For example you can just do nothing infinitely many times (literally identity operation of a group).
Cope. That's not doing anything.

Anonymous

Anonymous Tue 08 Dec 2020 17:01:46 No.12435153 Report

Quoted By:

>>12435142
>How?
I just gave two examples.
>>12433324
and the identity operation
>That's not doing anything.
yes, that's called the identity operation

Anonymous

Anonymous Tue 08 Dec 2020 17:49:03 No.12435391 Report

Quoted By: >>12435454 >>12436852

>>12435139
>you can just do nothing infinitely many times
It's not infinity if you can stop and do something else.

Anonymous

Anonymous Tue 08 Dec 2020 17:55:21 No.12435432 Report

Quoted By:

Hitomi’s number. b/c there is a count limit eventually it will end to two.
1+1/2+1/4+1/8+1/16+...
1/2^n [0,N]
1/2^h = 1/h =0
this is because of the count limit.
Reals and naturals are finite.

Anonymous

Anonymous Tue 08 Dec 2020 17:59:12 No.12435454 Report

Quoted By: >>12435515 >>12436852

>>12435391
why? I can do nothing infinitely many times, stop, then do something else. Jesus, why do brainlets stuggle with vacuous statements so much?

Anonymous

Anonymous Tue 08 Dec 2020 18:02:34 No.12435482 Report

Quoted By: >>12435487

am i banned haha

Anonymous

Anonymous Tue 08 Dec 2020 18:03:19 No.12435487 Report

Quoted By:

>>12435482
Yes, we have banned you. Hope you learn from your missed steaks.

Anonymous

Anonymous Tue 08 Dec 2020 18:08:38 No.12435515 Report

Quoted By: >>12435595 >>12436852

>>12435454
>I can do nothing infinitely many times
No, you can't. That's nonsense. You can never do something, and equate it to what you're saying through commutativity, but by definition you can't do something forever and then stop.

Anonymous

Anonymous Tue 08 Dec 2020 18:08:48 No.12435521 Report

Quoted By:

>>12431247
>he got filtered by fucking zeno
oh nononono nooo

Anonymous

Anonymous Tue 08 Dec 2020 18:09:42 No.12435528 Report

Quoted By:

>>12431247
After a certain decrease in length between you and the turtle, quantum particles can just say fuck it and decide you reached the turtle. Concepts like size, speed, position, etc. Only exist relative to other things, and in the realm of a single elementary particle, there is zero distinction.

Anonymous

Anonymous Tue 08 Dec 2020 18:11:43 No.12435547 Report

Quoted By:

>>12431350
There is a smallest quantifiable "reliable" state, which is the interaction between two elementary particles. Once you go down to a single particle, there is no definable size.

Anonymous

Anonymous Tue 08 Dec 2020 18:19:13 No.12435595 Report

Quoted By: >>12435661

>>12435515
I'm not equating anything to what I'm saying through commutativity. I'm giving you an example.
>No, you can't.
why not?
>That's nonsense.
filtered

Anonymous

Anonymous Tue 08 Dec 2020 18:31:59 No.12435661 Report

Quoted By: >>12435764 >>12436852

>>12435595
>I'm not equating anything to what I'm saying through commutativity.
No shit. If you did, you'd stop being wrong.
>I'm giving you an example.
You can't perform the identity function an infinite number of times and then stop performing it, you fucking moron. Infinity doesn't end.

Anonymous

Anonymous Tue 08 Dec 2020 18:49:56 No.12435764 Report

Quoted By: >>12435785

>>12435661
>Infinity doesn't end
infinity doesn't begin either. Performing operations a certain number of times does not necessitate a temporal or spatial element to it, so there's no necessity in things like "begin" or "end". What you're doing is thinking about it with grug logic of "me do thing once every 1 second, so it must be big number of second put inside a small number. Grug thinks impossible."

Anonymous

Anonymous Tue 08 Dec 2020 18:53:41 No.12435785 Report

Quoted By: >>12435809

>>12435764
>infinity doesn't begin either.
Right, that's why there's no least natural number. Just stop digging, fool. You have no clue what you're talking about.

Anonymous

Anonymous Tue 08 Dec 2020 18:58:17 No.12435809 Report

Quoted By: >>12435892

>>12435785
I'm not talking about sets, I'm talking about the necessity of associating mathematical operations with space and time. You don't have to do that. Your logic is "If I gotta do an action, I need to associate it with a certain interval of time to do it", whereas I'm saying that's not the case.

Anonymous

Anonymous Tue 08 Dec 2020 19:01:53 No.12435830 Report

Quoted By:

>>12431269
Someone must be an engineering major

El Arcón

View Same Google iqdb SauceNAO TIMESAND___7fkecopypastaBTFOed.png, 166KiB, 1131x656

El Arcón Tue 08 Dec 2020 19:11:53 No.12435876 Report

Quoted By:

Consider the paradox in the case of throwing a ball at a wall at constant velocity. If it takes time "t" for the ball to hit the wall (as computed by the distance to the wall divided by the ball's velocity), then the times related to the paradox are $\{t/2,\, 3t/4,\, 7t/8,\, 15t/16,\,\dots\,\}$ . This is a Cauchy sequence. Since the time sequence is Cauchy, infinite time will not accrue by the accumulation of the time steps in this sequence. Now matter how many time steps you add to this sequence, it will never exceed "t." However, a clock measuring the duration of the motion will eventually measure an elapsed time in excess of "t." Once the clock shows an elapsed time greater than "t," the ball will have traveled further than the distance to the wall if it has not hit the wall. Since it is impossible to travel past the wall without hitting it, the ball must have hit the wall at some time before the clock showed an elapsed time greater than "t."

Anonymous

Anonymous Tue 08 Dec 2020 19:14:07 No.12435892 Report

Quoted By: >>12435913

>>12435809
>I need to associate it with a certain interval of time
No, time has nothing to do with it. If you apply an identity transformation to an object "infinity" times, you can't do anything else to the object. If you want to do anything else, the best you can do is equate it to a new object, and start a new string of operations on the new object.

Anonymous

Anonymous Tue 08 Dec 2020 19:17:49 No.12435913 Report

Quoted By: >>12435931 >>12436002

>>12435892
>to an object "infinity"
>object "infinity"
>object
bruh
pick up an analysis book. Nowhere in there will you ever see such an "object" like "infinity" defined. There is no such thing.

Anonymous

View Same Google iqdb SauceNAO 038DF7BC-8805-4D69-907F-7F74D168 (...).jpg, 307KiB, 1080x1331

Anonymous Tue 08 Dec 2020 19:20:10 No.12435924 Report

Quoted By:

>>12431247

Anonymous

Anonymous Tue 08 Dec 2020 19:21:10 No.12435931 Report

Quoted By: >>12436021

>>12435913
you might see "?" defined

Anonymous

Anonymous Tue 08 Dec 2020 19:23:11 No.12435943 Report

Quoted By:

>>12431247

https://www.youtube.com/watch?v=tQSbms5MDvY

Anonymous

Anonymous Tue 08 Dec 2020 19:31:27 No.12436002 Report

Quoted By: >>12436021

>>12435913
>"object" like "infinity" defined
What the fuck are you even talking about? Is English not your first language? If it is, you're a literal imbecile.

Anonymous

Anonymous Tue 08 Dec 2020 19:33:52 No.12436021 Report

Quoted By: >>12436038 >>12436167 >>12436189 >>12436203 >>12436660 >>12437991

>>12435931
It's definitely not defined as an element in any set, and it's definitely not an element of the naturals, reals, or any other infinite set. The way we look at infinity in limits is through an epsilon-delta statement. The formal definition of a limit of a sequence is
$\forall\epsilon > 0 \exists N\in\mathbb{N}$ such that $\forall n \geq N$ $|x_n - x| < \epsilon$
>>12436002
>What the fuck are you even talking about?
basic math. Too advanced for idiots like you.
>Is English not your first language?
no

Anonymous

Anonymous Tue 08 Dec 2020 19:35:52 No.12436038 Report

Quoted By:

>>12436021
>If you apply an identity transformation to an object "infinity" times
Not him but read this and keep rereading it until you realize you are retarded

Anonymous

Anonymous Tue 08 Dec 2020 19:37:56 No.12436063 Report

Quoted By: >>12436088

This thread is proof that stemcels can't handle real problems. Zeno's paradoxes don't prove anything because logic is derived from observations of reality, therefore if a valid logical construct "disproves" reality, it just makes incorrect assumptions. Zeno says things that are possible are impossible, therefore his assumptions about the nature of motion must be incorrect.

Anonymous

Anonymous Tue 08 Dec 2020 19:40:19 No.12436082 Report

Quoted By:

>>12431247

Paradoxes and singularities often point out that something is off about the theory and that we are missing something. In the case of Zen's Paradoxes, is all about poking holes at Classic Greek Logic and Math.

Anonymous

Anonymous Tue 08 Dec 2020 19:40:49 No.12436088 Report

Quoted By: >>12436099

>>12436063
Zeno would tell you that what you are perceiving as "possible" is just an illusion of your senses that isn't to be trusted.

Anonymous

Anonymous Tue 08 Dec 2020 19:42:27 No.12436099 Report

Quoted By: >>12436105

>>12436088
Then how can his logic be trusted?

Anonymous

Anonymous Tue 08 Dec 2020 19:44:14 No.12436105 Report

Quoted By:

>>12436099

Greek logic is flawless. Reality is flawed.

Anonymous

Anonymous Tue 08 Dec 2020 19:56:19 No.12436167 Report

Quoted By: >>12436201

>>12436021
>t's definitely not defined as an element in any set, and it's definitely not an element of the naturals, reals, or any other infinite set. The way we look at infinity in limits is through an epsilon-delta statement. The formal definition of a limit of a sequence is
>??>0?N?N??>0?N?N such that ?n?N?n?N |xn?x|<?
it's an element of the extended number line

El Arcón

View Same Google iqdb SauceNAO TIMESAND___PNGhfhrllwl44rghrh8HI (...).png, 54KiB, 882x397

El Arcón Tue 08 Dec 2020 20:00:10 No.12436189 Report

Quoted By: >>12436201

>>12436021
>It's definitely not defined as an element in any set
The set R union {+infty,-infty} obtained by adjoining two improper elements to the set R of real numbers is normally called the set of (affinely) extended real numbers. Although the notation for this set is not completely standardized, R^_ is commonly used. The set may also be written in interval notation as [-infty,+infty]. With an appropriate topology, R^_ is the two-point compactification (or affine closure) of R. The improper elements, the affine infinities +infty and -infty, correspond to ideal points of the number line. Note that these improper elements are not real numbers, and that this system of extended real numbers is not a field.

Anonymous

Anonymous Tue 08 Dec 2020 20:03:07 No.12436201 Report

Quoted By: >>12436227

>>12436167
>>12436189
>extended number line
>extended reals
the most useless concept ever. Your group/semigroup axioms won't work, so you can throw away any assumptions you use about group, ring, or field structure of your algebra.
And get fucked, Tooker

Anonymous

Anonymous Tue 08 Dec 2020 20:03:12 No.12436203 Report

Quoted By: >>12436310

>>12436021
>no
Okay, then you're not necessarily an imbecile, but you're still clearly a brainlet. In that sentence, infinity refers to an object being endlessly mapped through your "identity function," not to the object itself.

Anonymous

Anonymous Tue 08 Dec 2020 20:05:37 No.12436227 Report

Quoted By: >>12436244

>>12436201
>the most useless concept ever. Your group/semigroup axioms won't work, so you can throw away any assumptions you use about group, ring, or field structure of your algebra.
extended reals are not about the algebra, but about the topology. you're useless.

Anonymous

Anonymous Tue 08 Dec 2020 20:07:32 No.12436244 Report

Quoted By: >>12436306

>>12436227
I can only thing of projective spaces as something where such a thing would be useful topologically. Do you have any other examples?

Anonymous

View Same Google iqdb SauceNAO st,small,507x507-pad,600x600,f8f (...).jpg, 37KiB, 600x600

Anonymous Tue 08 Dec 2020 20:20:57 No.12436306 Report

Quoted By: >>12436317

>>12436244
it BTFOs the "it gets close but never reaches hurr durr" brainlets. just define the limit of a sequence as the unique continuous extension to $\mathbb{N} \cup \{ \infty \}$ evaluated at $\infty$ . every limit is reached that way.

Anonymous

Anonymous Tue 08 Dec 2020 20:21:17 No.12436310 Report

Quoted By: >>12436465

>>12436203
>endlessly mapped
what does that mean? Do you mean mapping from an infinite domain? Where's the problem in that? Ok, let's go over what you said.
>If you apply an identity transformation to an object "infinity" times, you can't do anything else to the object.
anything else in what sense? Anything else while I'm doing the operations? Is this in a sense of order of operations or in a temporal sense?
>If you want to do anything else, the best you can do is equate it to a new object, and start a new string of operations on the new object.
equating something is an equivalence relation. There is no difference in two objects if they're actually equal. You're just mentally separating them.

Anonymous

Anonymous Tue 08 Dec 2020 20:22:31 No.12436317 Report

Quoted By: >>12436497

>>12436306
>just define
why? What advantage does it give besides the contrarian schizo "muh infinitesimals can't exist REEEEEEEEEE"?

Anonymous

Anonymous Tue 08 Dec 2020 20:34:41 No.12436382 Report

Quoted By: >>12436448

There is no such thing as "zero" in real life.
Zero is just a concept of human imagination.
The same way a hole isn't a real thing, it's an emergent property of topology.
Emptiness is freedom for imagination.

Anonymous

Anonymous Tue 08 Dec 2020 20:48:40 No.12436448 Report

Quoted By:

>>12436382
if we're looking by the use case, zero is just a way for us to say that something is lacking
it's still better than negatives

Anonymous

Anonymous Tue 08 Dec 2020 20:51:45 No.12436465 Report

Quoted By: >>12436478 >>12436497

>>12436310
>anything else in what sense?
If the mapping ends, then there must be a last mapping, so by definition it wasn't mapped an "infinite" number of times. It was mapped it an arbitrarily large, finite number of times. I don't know what "infinity" means in your native language, but in English it means that there is no last mapping.

Anonymous

Anonymous Tue 08 Dec 2020 20:54:56 No.12436478 Report

Quoted By: >>12436491

>>12436465
wtf does it mean for a mapping to end? What are you on about? Do you know how functions work? We relate elements of one set to elements of another. There is no order in which we have to relate them. As long as a mapping is well-defined, we're good.

Anonymous

Anonymous Tue 08 Dec 2020 20:58:43 No.12436491 Report

Quoted By: >>12436539 >>12436622

>>12436478
It's fine to map something an infinite number of times, but you can't then perform any other operations on the same object. If you try to, without equating it to a new object, then your mapping wasn't infinite, it was finite.

Anonymous

Anonymous Tue 08 Dec 2020 20:59:46 No.12436497 Report

Quoted By: >>12436539 >>12436622

>>12436317
check this out. with my definition, I can totally btfo this post >>12436465
>If the mapping ends, then there must be a last mapping, so by definition it wasn't mapped an "infinite" number of times
my definition certainly has a "last mapping" and yet it was "mapped infinitely many times"

Anonymous

Anonymous Tue 08 Dec 2020 21:07:27 No.12436539 Report

Quoted By: >>12436641 >>12437181

>>12436491
Jesus.... you retard, when you say a=b, that means they're one and the same. There's no such thing as a "new object". By your logic if I say a+b=c and then say c+d=f, then a+b+d=f is something different than c+d=f.
>>12436497
nobody cares about your definition. If you're talking about "mapping" something, people assume you mean you're defining a function from some set to another. A formal definition of a function is the following:
Let A and B be sets. A function $f : A \rightarrow B$ is a subset of a Cartesian product $A\times B$ , such that
1. $\forall a\in A\exists b\in B$ such that $(a,b)\in f$
2. if $(a,b) \in f$ and $(a,c) \in f$ , then b = c.
Do you see anything here that says "hurr durr muh mapping ends/begins"?

Anonymous

Anonymous Tue 08 Dec 2020 21:19:04 No.12436622 Report

Quoted By: >>12436671

>>12436491
>>12436497
You're both idiots. You can't take the "infinitieth" element of am infinite list, you fucking brainlets. There's no element "number infinity." You can take the limit of that infinite list, equate a new element to it, and move on from there, but you can't take the "last element" of an infinite list.

Anonymous

Anonymous Tue 08 Dec 2020 21:21:54 No.12436641 Report

Quoted By: >>12436660

>>12436539
You're the retard, dipshit. The limit of an infinite list isn't the "last element," you fucking latex pseud.

Anonymous

Anonymous Tue 08 Dec 2020 21:24:56 No.12436660 Report

Quoted By: >>12436679

>>12436641
who the fuck said it was? I gave you the definition of a limit here >>12436021
where the fuck do you see something like "the last element" in there?

Anonymous

Anonymous Tue 08 Dec 2020 21:26:29 No.12436671 Report

Quoted By: >>12436694

>>12436622
you couldn't be more wrong, silly. consider the following
$(0,1)$ is an infinite set which doesn't have a first nor last element
$[0,1)$ is an infinite set which has a first element but not a last element
$(0,1]$ is an infinite set which doesn't have a first element but does have a last element
$[0,1]$ is an infinite set which has both first and last element
the set $\mathbb{N} \cup \{ \infty\}$ also has a first and a last element. however the set has a second element, but not a penultimate element. this is the set for you if you want to see what happens to things after "infinite number of steps".

Anonymous

Anonymous Tue 08 Dec 2020 21:28:47 No.12436679 Report

Quoted By: >>12436691 >>12436809

>>12436660
Who the fuck are you? Anonymous? The argument I've been having for the last 10 posts or whatever is about whether or not you can perform an infinite number of mappings through the identity function and then perform other operations on the same element. If you're not the guy I'm arguing with then fuck off with your extraneous peanut gallery shit.

Anonymous

Anonymous Tue 08 Dec 2020 21:29:53 No.12436691 Report

Quoted By: >>12436707

>>12436679
lmao do you want a room just for the two of you guys?

Anonymous

Anonymous Tue 08 Dec 2020 21:30:25 No.12436694 Report

Quoted By: >>12436731

>>12436671
Retard, not only is that not what we're talking about, why don't you try defining the mapping function that maps through every element in (0,1] and the ENDS at 1. Dumb fuck.

Anonymous

Anonymous Tue 08 Dec 2020 21:31:30 No.12436707 Report

Quoted By:

>>12436691
No, do you? You seem to think everyone is talking about some asinine post you made two hours ago.

Anonymous

Anonymous Tue 08 Dec 2020 21:34:11 No.12436731 Report

Quoted By: >>12436769

>>12436694
>why don't you try defining the mapping function that maps through every element in (0,1] and the ENDS at 1
do you mean like the identity function?

Anonymous

Anonymous Tue 08 Dec 2020 21:37:34 No.12436767 Report

Quoted By:

>>12431247
What makes it a "paradox" is the mistaken believe that infinite limits can't "reach" their limit in a finite time.

Anonymous

Anonymous Tue 08 Dec 2020 21:38:03 No.12436769 Report

Quoted By: >>12436789

>>12436731
Lmfao, tell me more about your identity function that doesn't map an element to the same element.

Anonymous

Anonymous Tue 08 Dec 2020 21:40:55 No.12436789 Report

Quoted By: >>12437062

>>12436769
apparently identity function is controversial in this thread, lol. so do you mean like $f(x) = x^2$ ?

Anonymous

Anonymous Tue 08 Dec 2020 21:44:51 No.12436809 Report

Quoted By: >>12437062

>>12436679
and the argument I've been having is that no such fucking thing as ordering comes up when you're mapping something. You're saying shit that doesn't make any sense. Either try to clearly define your terms and not confuse them with common terms used in math or get fucked. You haven't said a single argument against that possibility. You wanna see a magic trick? Watch this:
$a + (\sum_{n=0}^\infty 0) + c = a + c$
WOW ABSOLUTELY MINDBOGGLINGLY IMPOSSIBLE

Anonymous

Anonymous Tue 08 Dec 2020 21:53:47 No.12436852 Report

Quoted By: >>12437062

all right, correct me if I got this wrong:

>>12433324
>>12435139
>>12435454
this anon knows what he's talking about

>>12435391
>>12435515
>>12435661
this one's a schizo

Anonymous

Anonymous Tue 08 Dec 2020 22:16:45 No.12437062 Report

Quoted By: >>12437113 >>12437122

>>12436809
>>12436789
>>12436852
You stupid fucks, none of that has anything to do with putting an element through an infinite number of mappings and then performing an operation on the last element. Fucking illiterate pseuds

Anonymous

Anonymous Tue 08 Dec 2020 22:20:09 No.12437113 Report

Quoted By: >>12437140

>>12437062
>putting an element through an infinite number of mappings and then performing an operation on the last element
are you saying this is impossible?

Anonymous

Anonymous Tue 08 Dec 2020 22:20:49 No.12437122 Report

Quoted By: >>12437140

>>12437062
I don't think you know what a mapping is, anon.

Anonymous

Anonymous Tue 08 Dec 2020 22:22:27 No.12437140 Report

Quoted By: >>12437181

>>12437113
Yes.
>>12437122
Enlighten me, retard.

Anonymous

Anonymous Tue 08 Dec 2020 22:24:21 No.12437181 Report

Quoted By: >>12437212

>>12437140
you're very welcome, sweety
>>12436539

Anonymous

Anonymous Tue 08 Dec 2020 22:26:34 No.12437212 Report

Quoted By: >>12437245

>>12437181
Jesus christ you imbecile, you’re even dumber than the other guy who didn’t speak English. At least he had an excuse.

Anonymous

Anonymous Tue 08 Dec 2020 22:28:32 No.12437245 Report

Quoted By: >>12437555

>>12437212
First of all, I am "that guy", and secondly, can you tell me why I'm supposedly an imbecile? Is it because you're too dumb to comprehend the definition of a map/function? I can walk you through it, sweetheart, it's ok.

Anonymous

Anonymous Tue 08 Dec 2020 22:40:00 No.12437555 Report

Quoted By: >>12437641

>>12437245
Lol, then you have no excuse. That has nothing to do with performing an infinite number of identity transformations on an object, and then taking the last element of that infinite succession. You lost and decided to change the subject, fuck off lmao.

Anonymous

Anonymous Tue 08 Dec 2020 22:46:27 No.12437641 Report

Quoted By: >>12437673

>>12437555
you were the retard who started throwing the term "mapping" around, you cunt. Which is why I spent the last 10 fucking posts trying to comprehend what in the fucking world you mean by that word, because in actual mathematics, the word "mapping" has a precise meaning which I gave to you. This isn't your high school English literature essay. Use your terms precisely instead of trying to sound smart.

Anonymous

Anonymous Tue 08 Dec 2020 22:50:42 No.12437673 Report

Quoted By: >>12437708

>>12437641
Shut the fuck up pseud, a function literally maps from one element to another. You lost because you’re stupid, and now you’re just flailing around writing non sequiturs. Stick to trolling.

Anonymous

View Same Google iqdb SauceNAO facepalm_pepe.png, 7KiB, 234x215

Anonymous Tue 08 Dec 2020 22:55:45 No.12437708 Report

Quoted By: >>12437753

>>12437673
>a function literally maps from one element to another
you win. I cannot recover from this. How more rigorous and precise can one get? My definition is inferior in every sense and definitely doesn't state this exact fucking thing, but in proper set notation. Next time, please, don't argue about math if you don't know math.

Anonymous

Anonymous Tue 08 Dec 2020 23:02:48 No.12437753 Report

Quoted By: >>12437785 >>12437805

>>12437708
Retard, your non sequitur has nothing to do with performing an infinite number of identity transformations and then taking the last element of that succession. Give up.

Anonymous

View Same Google iqdb SauceNAO 1542237869693.gif, 376KiB, 500x491

Anonymous Tue 08 Dec 2020 23:04:06 No.12437767 Report

Quoted By:

>>12431247
/SCI/TODDLERS BTFO
If we take the example literally, whether or not we ever solve “the universe is continuous or smooth” debate doesn’t matter. If it’s a physical problem, we will never be able to measure below a certain point with certainty.
But if it’s a math problem, then it’s just a door into exploring limits.
The retards ITT arbitrarily switch back and forth to shitpost.

Anonymous

Anonymous Tue 08 Dec 2020 23:05:53 No.12437785 Report

Quoted By:

>>12437753
sure. This does though.
$a + (\sum_{n=0}^infty 0) + c = a + c$
(hint 1: 0 is the identity element of addition)
(hint 2: any group identity is commutative, whether the group is commutative or not)
Now please, just stop embarrassing yourself.

Anonymous

Anonymous Tue 08 Dec 2020 23:08:50 No.12437805 Report

Quoted By: >>12437842

>>12437753
sure. This does though.
$a+(\sum_{n=0}^\infty 0)+c=a+c$
(hint 1: 0 is the identity element of addition)
(hint 2: if you're worried about commutativity of some action, then any group identity is commutative, whether the group is commutative or not)
Now please, just stop embarrassing yourself.

Anonymous

Anonymous Tue 08 Dec 2020 23:14:37 No.12437842 Report

Quoted By: >>12437893

>>12437805
That looks suspiciously like you’re taking the LIMIT of the infinite list and equating that LIMIT to a new element, you fucking dipshit, which is literally what I told you you had to do. Are you going to pay me for the lesson now?

Anonymous

Anonymous Tue 08 Dec 2020 23:21:30 No.12437893 Report

Quoted By: >>12437950

>>12437842
and where do you see a limit there? Infinite sums are formed inductively, no need for limits. Again, don't say shit if you don't know what you're saying.

Anonymous

Anonymous Tue 08 Dec 2020 23:22:28 No.12437901 Report

Quoted By:

>>12431316
That is not zeno's paradox. The statement does not mention time, only the distance travelled. Which is actually the reason it's not a paradox because the velocities never change. So you may have travelled half the distance but you have done so in half the time.

Anonymous

Anonymous Tue 08 Dec 2020 23:28:40 No.12437950 Report

Quoted By: >>12437991

>>12437893
There’s no last element in an infinite series, you idiot. It doesn’t matter how you define the new element you’ve equated to the sum. You’re taking a new element, not the last element of the fucking infinite series, moron.

Anonymous

Anonymous Tue 08 Dec 2020 23:39:07 No.12437991 Report

Quoted By: >>12438002

>>12437950
yes, indeed. Again, where is the limit there? Look at the definition of a limit in >>12436021
and tell me where this ever comes up in the proof I will now give that this infinite sum is just equal to zero. I'll be as rigorous and as formal just to annoy you because you seem to be triggered by that. Here we go
Proposition: $sum_{n=0}^\infty 0 = 0$
Proof: We will induct on n.
Base case: n = 0
We have
$\sum_{n=0}^0 0 = 0$
which holds trivially.
Inductive hypothesis:
Suppose the proposition holds for some $k$ , that is
$sum_{n=0}^k 0 = 0$
Now consider the case for $k+1$
$sum_{n=0}^{k+1} 0 = 0 + sum_{n=0}^k 0 = 0 + 0 = 0$
by the identity property of zero in the naturals. Therefore we can conclude that
$sum_{n=0}^n 0 = 0$
holds for all $n\in\mathbb{N}$ by induction, and thus
$sum_{n=0}^\infty 0 = 0$
QED

Anonymous

Anonymous Tue 08 Dec 2020 23:40:10 No.12438002 Report

Quoted By: >>12438041 >>12438060

>>12437991
fucked up the typesetting, but whatever. You get the idea. /sci/ really needs a LaTeX preview option.

Anonymous

Anonymous Tue 08 Dec 2020 23:48:05 No.12438041 Report

Quoted By: >>12438084

>>12438002
Don’t worry about your latex, it’s the least of your problems. Focus on the fact that you keep losing the argument and trying to change the subject.

Anonymous

Anonymous Tue 08 Dec 2020 23:51:01 No.12438060 Report

Quoted By: >>12438084

>>12438002
> /sci/ really needs a LaTeX preview option.
It has one. That is what the TeX button is in the top left of the reply window.

Anonymous

Anonymous Tue 08 Dec 2020 23:54:11 No.12438084 Report

Quoted By:

>>12438041
ok, whatever
>>12438060
thanks, dude. Never really noticed it.

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches