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/sci/ - Science & Math

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10786214 No.10786214 [Reply] [Original]

There are an infinite number of numbers between 1 and 2, 2 and 3, and so on. This means infinity doesn't imply there can be no limit. What objectively is the difference between defining the first number of an infinite set and the last number? Just as the first number of .999... is defined as 9, and how the last number of the infinity between 1 and 2 is defined as 2, or the last number of the infinity between 2 and 3 is defined as 3, why can't there be a .999... where the last number is defined as 8?
You should know the answer is necessarily invokes metaphysical logic, therefore please spare me the pretense of saying anything meaningful under the guise of math that necessarily presupposes metaphysical assumptions and circular reasoning.

>> No.10786353

>>10786214
>why can't there be a .999... where the last number is defined as 8?
There is no last number in 0.999...
It's fundamentally different from [1, 2]
The question is nonsensical

>> No.10786357

>>10786353
>It's fundamentally different from [1, 2]
>The question is nonsensical
Show me.

>> No.10786366

>>10786214
It's infinite you can divide a number an infinite number of times.

>> No.10786392

>>10786214
>Just as the first number of .999... is defined as 9, and how the last number of the infinity between 1 and 2 is defined as 2
You're conflating two different things. .999... is a decimal representation of a number whose first digit is 9. "The infinity between 1 and 2" is a set of numbers, the highest of which is 2. The rest of your post is standard /sci/ word salad and I can't tell what you're trying to argue, but if you want a rigorous understanding of this stuff you should consider real analysis.

>> No.10786413

>>10786214
i have no idea what you are trying to say. sets and infinite numbers are different things. And you cant define .9999999... with an 8 "at the end" because the ... means there is no end.

>> No.10786419

>>10786357
0.999... is a list without an end

The numbers in [1,2] can't be listed (they're uncountable).

>> No.10786435

>>10786214
The digits in 0.999... form a sequence. The set [1, 2] is an interval. Those are two entirely different things, and carelessly trying to apply concepts from one to the other leads to nonsense.

>> No.10786440 [DELETED] 

>>10786392
>>10786413
I'm not confusing anything; I simply question whether the distinction between sets and infinite numbers only exists only in your mind. The rest of this post is asking not to employ exactly this sort of rhetorically-tautological circular reasoning. An infinity can be contained within a set, therefore an infinity can have limits, therefore the notion that .999... can have a designated first number but can't a designated a last is what seems nonsensical. Your intuitive understanding of how this is possible is not necessary for the symbolic designation of this concept in language, which is potentially useful.

>> No.10786448 [DELETED] 

>>10786392
>>10786413
I'm not confusing anything; I simply question whether the distinction between sets and infinite numbers only exists only in your mind. The rest of this post is asking not to employ exactly this sort of rhetorically-tautological circular reasoning. An infinity can be contained within a set, therefore an infinity can have limits, therefore the notion that .999... can have a designated first number but not a designated a last is what seems nonsensical. Your intuitive understanding of how this is possible is not necessary for the symbolic designation of this concept in language, which is potentially useful.

>> No.10786450

>>10786392
>>10786413
I'm not confusing anything; I simply question whether the distinction between sets and infinite numbers only exists only in your mind. The rest of this post is asking not to employ exactly this sort of rhetorically-tautological circular reasoning. An infinity can be contained within a set, therefore an infinity can have limits, therefore the notion that .999... can have a designated first number but not a designated last is what seems nonsensical. Your intuitive understanding of how this is possible is not necessary for the symbolic designation of this concept in language, which is potentially useful.

>> No.10786480

>>10786440
.999 repeating infinitely is simply another way of writing the number 1.
Since the nines repeat infinitely, .999 repeating cannot, by definition, have any other number except 9 in it, forever.
Everything you know is a human construct, and, as such, is relative and ultimately arbitrary. But that doesn't necessitate that everything is vanity. For one, you should know the rules of infinite sets before you can effectively break them.
However, the only thing I know is that I know nothing.

>> No.10786595 [DELETED] 

>>10786480
>by definition
The entire point is that the definitions are irrelevant. If a symbol can designate, that an infinitely-repeating digit, such a designation shouldn't not exist merely because it doesn't fit some pre-established definition, or because you can't understand how it's possible. Objectively, an infinitely-repeating series having a first number is as possible or as impossible as it having a last number. There's no reason I shouldn't be able to write something like .999... [the other end is 8].

>> No.10786604

READ THIS ONE
fixed major error my brain incorrectly thought I had included
>>10786480
The entire point is that the definitions are irrelevant. If a symbol can designate that an infinitely-repeating digit "ends" with some other number, such a designation shouldn't not exist merely because it doesn't fit some pre-established definition, or because you can't understand how it's possible. Objectively, an infinitely-repeating series having a first number is as possible or as impossible as it having a last number. There's no reason I shouldn't be able to write something like .999... [the other end is 8]. - /pol/ post

>> No.10786606

>>10786214
So such thing as infinity.

>> No.10786616

>>10786450
all real numbers between 1 and 2 dont have a designated "last number" either, I still dont know what you are saying.
AS far as i can tell, it seems you need to understand what a limit is.

>> No.10786625

>>10786616
To avoid further pedantry, go ahead and replace "last number" whenever it occurs with "limit" in your mind.

>> No.10786632

the limit of 1.9999.... is 2, which is why .9999...=1. We define infinite numbers or sums as their limit. i still dont know what you are saying

>> No.10786635

>>10786625
>>10786632
meant to reply

Can you elaborate? I still dont understand what you are saying?

>> No.10786639

>>10786214
This is the kind of shit that the retarded drug dealer senior in my freshman high school math class would say

>> No.10786687
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10786687

>>10786604
Take the numbers between 0 and 1 for example:

1/2 = 0.5
0.5/2 = .25
.25/2 = 0.125
0.125/2 = 0.625
0.625/2 = 0.03125

You can continue to divide your results an infinite amount of times and the result will always fall between 0 and 1 which means there are an infinite amount of numbers between 0 and 1

>> No.10786712

>>10786687
Could we prove whether or not that the last digit at the end of this sequence repeated forever would be a 5 like all it's finite predecessors seem to be, despite it approaching zero?

>> No.10786731

>>10786687
When comparing to geometry, e.g. rays and line segments, I concede that I may be wrong about designating an "end" digit for something like .999... making sense; it would be analogous to a line segment. However, this leads me to contend that the "ray" should be able to travel the "other way," e.g. I should be able to define something that might look like ...999, which would be the number right next to 1 (having the side-effect of .999... not "just being another way to write" 1), theoretically if not conceivably. This may warrant its own thread at another time.

>> No.10786749

>>10786712
>thereby proving an infinitely-repeating digit can asymptotically approach its limit without ever becoming that limit-number, i.e. that .999... does not necessarily = 1
I'd be interested in this proof as well. I doubt anyone will oblige. .999... = 1 is reminiscent of 666 trying to be 7, or satan trying to be like God (back then they used base-7, so 7 was their 10, so to speak). The proof is in how valiantly atheists in particular, not just agree, but absolutely insist .999... = 1. Satan would try to infest every way we think, including in logic.

>> No.10786750

>>10786687
More...

>> No.10786753

>>10786214
What the fuck is that thing

>> No.10786781

>>10786753

It's clearly a musician dressed up flamboyantly for a concert performance. I'm not sure (because I'm not familiar with the band or its live routine), but I'm about 80% confident that it's Wayne Coyne, lead singer of The Flaming Lips. I've seen a pic or two where he wears flamboyant getups like these for shows.

>> No.10786783

>>10786450
What are you even trying to say?

>> No.10786794

>>10786783
must be nothing, 'cause there's no way you're just retarded

>> No.10786805
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10786805

>>10786450
>the notion that .999... can have a designated first number but not a designated last
Can you quote anyone ever who has claimed that?

>> No.10786818

>>10786450
>An infinity can be contained within a set, therefore an infinity can have limits, therefore the notion that .999...
I don't think you understand what infinity is, pal

>> No.10786819

>>10786604
Yes, mathematics is what we define it to be. Your point is...?

>> No.10786824

>>10786712
there isn't a number at the end of the sequence, anon. It is an infinite sequence, after all.

>> No.10786849

>>10786805
I don't have time for your stupidity. Just go ahead an provide an example of otherwise and say I'm wrong, instead of assuming your question is somehow an argument.
>>10786818
"without finitude." Now go ahead and say something lucid, pal.
>>10786819
That those definitions endeavor to be a reflection of reality, and that reality dictates the definitions should be changed. If you're going to pose nothing but weak semantics and more questions to which you hope I have no answer, shut the fuck up already and leave the thread, idiot.
>>10786824
Limit and end are synonymous here. Pedantry will get you no where good.

>> No.10786868

>>10786849
>"without finitude." Now go ahead and say something lucid, pal.
I stand by my comment. Infinity is not a number, but a concept. Infinity cannot be "contained" within a set. What you are referring to is an infinite set, which is pretty different from what you said before.

>> No.10786873

>>10786849
>Limit and end are synonymous here. Pedantry will get you no where good.

alright, if by 'end' you are talking about the limit (which are very different things, but ok) than the the limit will be 0, and therefore will not have a 5 digit at the end.

>> No.10786874

>>10786868
What difference is there between the two that would contradict anything I've said? Pedantry itself doesn't constitute an argument.

>> No.10786881

haha stupid muricans can't count

>> No.10786883

>>10786873
So your proof is that because the limit is 0, there will not be a 5 at the end? That's like saying "By definition, it must end in 0, therefore such is the case." That is not proof.

>> No.10786884

>>10786849
>That those definitions endeavor to be a reflection of reality, and that reality dictates the definitions should be changed. If you're going to pose nothing but weak semantics and more questions to which you hope I have no answer, shut the fuck up already and leave the thread, idiot.
I'm sorry to say this brovinsky but I think you are the idiot here. Mathematics, by definition, is what we define it to be. How 'reality' can reveal the answers to wheter there is the number 0.99..8? We cannot measure with an infinite precision, you realize that, right? When you say 'reality' I think what you mean is 'what I want it to be' which reveals that your insulting of others and asking meaningless questions is just the whining of a brainlet.

>> No.10786887

>>10786883
So your proof is that because the limit is 0, there will not be a 5 at the end? That's like saying "By definition, it must end in 0, therefore such is the case." That is not proof.
That is exactly what I am saying. Mathematics is what we define it to be, retard.

>> No.10786893

>>10786883
I urge you to learn the formal definition of a limit. You will then realize that your question was a bit meaningless.

>> No.10786897

>>10786884
Reality does not imply measurability, idiot. Mathematical rules, they all, are meant to represent reality. If problems of involving infinities are not accurately representative of physical or metaphysical reality, that should be remedied. What you define on your lonesome is the stuff of subjective relativism, not I. Try not to project so obviously in your accusations.
>>10786893
Why not just copy-paste the "formal" definition

>> No.10786900

>>10786897
>Why not just copy-paste the "formal" definition
Holy shit, you can't even google the fucking definition?

https://en.wikipedia.org/wiki/(%CE%B5,_%CE%B4)-definition_of_limit

>> No.10786902

>>10786897
alright genius, how the fuck do you realize what reality thinks of you 0.99..8 number without measurement, huh? Ask the fucking skies?

>> No.10787005

>>10786214
The string of numbers between 1 and 2 is infinite but the magnitude is infinitesimal which is different

>> No.10787763

why do brainlets flock to infinity like flies on shit
>here is an infinite sequence
>what is the last element in the infinite sequence

this shit was rigorously established about 100 years ago by people who actually got things done
take your meds and fuck off