/sci/ - Science & Math

>>11745385
you forgot to say that 0.999... is between and 0 and 1 therefore 0.999... < 1

>>11745510
It's better to let them reach that realization on their own.

Light can illuminate dark areas and allow people to see things, but if the light is too powerful and comes on unexpectedly and too suddenly, then it can be blinding and feel painful, harsh and disorienting – causing the individual to close his eyes and turn away.

Is this the thread where people who can't understand limits gather?

Just stop it. You're embarrassing yourselves.

Imagine not being able to grasp a simple definition that's to be found in literally every rigorous elementary analysis textbook.
pic related is baby Rudin

The core of the mental problem in their minds of those who believe less than 1 is the same as 1 is this:

Their inability to comprehend that ".999..." isn't the same as "1" is directly tied to their inability to grasp eternity and infinity. Their minds have been programmed to believe eternity and infinity are impossibilities. Over the course of many generations of indoctrination into an alien worldview, their parents and their parents etc gradually "learned" to be unable to comprehend it and this "learned disability" was inherited, and encouraged/fueled by various external factors from the echoing modern culture.

So basically, they're mentally damaged.

This difficulty they have with eternity/infinity shows up in many different fields, from math to astrophysics.

This mental handicap is inherited directly from the (((Abrahamic))) religions, more specifically (((Christianity))) for us Westernerns. In it's origin, the inability to understand infinity and eternity is 100% Judaic in thought/philosophy. In contrast, the non-Jewish man; the Pagan man, at least the /European/ Pagan man, never had any problem with infinity and eternity. (((Christianity))) introduced into the minds of people the idea of life and the world/universe being linear, starting from point A and ending at a point B, whereas in the Native European worldview everything is an infinite circle.

That's why many people today can't understand that .999 repeating forever will never reach 1 - they refuse to accept the idea of an infinite/eternal repetition. Saying "it's 1" is their method of escaping from the uncomfortable (and to them insurmountable) challenge which the concept of infinity/eternity is to their Judaically-induced mental disease.

>>11745510
1/3 = 0.3333....
0.3333...*3 = 0.99999...
1/3*3 = 1
ergo 0.9999... = 1

>>11745809
>Their minds have been programmed to believe eternity and infinity are impossibilities
literally the opposite. When you DO understand infinity is when you see that .999... is exactly equal to 1. Those who think it's less are those who don't understand infinity, because they think things like 0.000....1 make any sense at all

>>11745809
Very related, a revealing admission by one of the believers in the "less than 1 = 1" meme.

>>11745845
Infinity is real. Therefore, 0.999... (an infinite amount of 9s) will never reach 1. It will forever approach it. Never equal it.

>>11745886
An infinite amount of 9's is equal to 1, it doesn't "approach" anything it's already there.

>>11745886 this is true
0.999... ≈ 1 this is true
0.999... = 1 this isnt true

>>11745939
SHUT THE FUCK UP U STUPID NIGGER WHAT IS BIGGER 0.999.. * infinity OR 1 * infinity???? U SAYIN' THIS IS THE SAME? I THOUGHT NOT U STUPID FUCK, ONE IS BIGGER IF ITS BIGGER ITS NOT THE SAME .

>>11746012
Wrong

>>11745791
>Rudin
Pic related.

> Native European worldview:
Infinity and eternity is real, the universe has always existed, less than 1 isn't the same as 1

> Jewish worldview:
Infinity and eternity isn't real, the universe was created by Yahweh/God/Allah or in a Big Bang, less than 1 is the same as 1

>>11746105
Those are both undefined.

>>11746130
>less than 1 isn't the same as 1
No one is disagreeing.

>>11745939
>An infinite amount of 9's is equal to 1
Nope. Just like a few tens of thousand does not equal 6 million.

>>11746185
Two proofs:

Via Cauchy sequences:

0.999... = (0.9, 0.99, 0.999,...) = lim as n-> inf of 1-1/10^n = 1

Via Dedekind cuts:

Assume to contradiction that x is a rational number such that

0.999... < x < 1

0.999... is greater than any finite string of 9s so for any natural number n

1-1/10^n < 0.999... < x < 1

1-x < 1/10^n

10^n < 1/(1-x)

n < log(1/(1-x))

Let n = ceiling(log(1/(1-x)))+1

ceiling(log(1/(1-x)))+1 < log(1/(1-x))

This is a contradiction, so x does not exist and 0.999... = 1.

>>11745939
You've admitted the amount of 9s are infinite. That's a good first step. The amount of 9s being infinite means "0.999..." is /forever/ less than 1. Everyone who isn't stuck with a dogmatic belief can plainly see this.

>>11746223
Meaningless equations doesn't a proof make.
>0.999... = 1.
Sorry bro, less than 1 isn't the same as 1.

>>11746225
>The amount of 9s being infinite means "0.999..." is /forever/ less than 1.
Proof? Also I don't see how "forever" is necessary since the properties of a number don't change in time.

>>11746243
>Meaningless equations doesn't a proof make.
Agreed. Which equation is meaningless?

>Sorry bro, less than 1 isn't the same as 1.
Agreed.

>>11746243
0.9999.... is not less than 1

>>11746140
I just wanted to find a way to put into words how to describe a small (even infinitly small) difference adds up over time making the lines of 1 and 0.999... diverge over (an infinte amount) of time. Thus they are not the same, thus the fucking = symbol musn't be used. I can't describe the amount of autism I have for using = signs if its not the fucking exact same thing its not the same. done. By accepting infinity you should accept an infinite smallness aswell so to say. It doesn't get rounded up, the difference is always there.

>>11746012
see>>11745814

>>11746286
infinitesimals do not exist in the Reals

>>11746286
>I just wanted to find a way to put into words how to describe a small (even infinitly small) difference adds up over time making the lines of 1 and 0.999... diverge over (an infinte amount) of time.
What does time have to do with anything? 0.999... doesn't change value over time. And the limit of its decimal truncations approaches 1.

>>11746274
It is.

"0.998" is less than 1.
"0.999" is less than 1.
"0.999...." is less than 1.

Just because the 9s are infinite doesn't mean they eventually reach 1. They don't. They never do. They're forever approaching 1. Eternally. Eternally - let that word sink in. Yes, eternally. You don't like that idea. Because Eternity is difficult for you to grasp. Because your worldview is Jewish.

>>11746359
>"0.998" is less than 1.
True
>"0.999" is less than 1.
True
>"0.999...." is less than 1.
False

>Just because the 9s are infinite doesn't mean they eventually reach 1.
What do you mean by "eventually?" If the 9s are infinite then the number equals 1. If not, then it doesn't equal 1.

>They're forever approaching 1.
The finite decimals approach 1, not the infinite decimals. You're just confusing the infinite for the finite.

It's like saying 3.14... is less than pi because the decimal truncations only approach pi. But 3.14... is pi exactly.

>>11746359
Excuse me, you didn't answer my question >>11746264

>>11746359
There is no "approaching" because the infinite amount of 9's is already there.
You're saying "the worldview is jewish" makes no sense, I dont even know what that means. Are you an electric universe faggot who believes the big bang didn't happen as well?

>>11746325
y = 0,999... x
y = x

you say these lines NEVER diverge?

>>11746610
Yes. y = (0.999...)x = x

See >>11746223

>>11746462
> If the 9s are infinite then the number equals 1.
They are repeating forever, meaning they never reach 1. It will get very "close" to 1, sure, and for practical purposes such as if you're measuring water or flour, it's good enough (for making a bread, 0.999... KG of flour will work just as fine as 1 KG). But number itself will never equal 1. It will get "closer" to 1 forever, eternally, but will never equal 1.

Less than 1 isn't the same as 1.

>>11746302
FUCK. this is kind of a fair point, but i think thats why you always use (1/3). how DOES this work, what do I read up to learn this. Becaues i've been thinking about these.. I don't know the exact term but infinitely repeating segments of numbers in fractions. And how I THINK that this changes in different base-numbers right? Enlighten me anon, i'm willing to switch sides here.

Holy KEK, in this thread the 0.999... = 1 tards are literally defending imaginary Jewish contructs such as the Big Bang idea.

Here's a history and reality lesson:

The Big Bang idea was originally invented by the Christian theologist Robert Grosseteste (1168-1253), first head of the university of Oxford. He had a vision that his Hebrew god Yahweh created a tiny spot of light that exploded rapidly taking the matter – which was simultaneously created by the god – with it to form a spherical universe.

Big Bang Cosmology in the modern sense was conjured up by the Christian Catholic priest Abbe Georges Lemaître.

The pioneering Nobel Prize winning plasma physicist and electrical engineer Hannes Alfvén said about Lemaître:

>I was there when Abbe Georges Lemaître first proposed this theory. Lemaître was, at the time, both a member of the Catholic hierarchy and a scientist. He said in private that this theory was a way to reconcile science with St. Thomas Aquinas' theological dictum of creatio-ex-nihilo (creation out of nothing).

>There is no rational reason to doubt that the universe has existed indefinitely, for an infinite time. It is only mysticism saying the universe was created - whether four thousand or twenty billion years ago.

>Since religion intrinsically rejects empirical methods, there should never be any attempt to reconcile scientific theories with religion. We must not confuse religion and science. An infinitely old universe, always evolving, isn't compatible with the Book of Genesis.

Lemaître is famous for his description of the beginning of the universe as "A Day without Yesterday" in reference to the Creation account in Genesis.

The Jew George Gamow, another famous Big Bang proponent, had no compunction in describing the graphs of conditions in the Big Bang as "Divine Creation Curves" and sent a copy of his book "The Creation of the Universe" to the then Pope.

[continued below...]

>>11746724

[continued]

In January 1933, the Christian priest Abbe Georges Lemaître travelled with the Jew Albert Einstein to California for a series of seminars. After the priest Lemaître detailed his Big Bang theory, the Jew Einstein stood up, applauded, and said:
>This is the most beautiful and satisfactory explanation of Creation to which I have ever listened.

Thus Big Bang is theology and mysticism, not science. Lemaître allowed his theological convictions to predetermine the outcome of a scientific inquiry. This violates the scientific method. Furthermore, the Big Bang creatio-ex-nihilo Creationism consists of a universe that's entirely filled by a continuous indivisible distribution of mass with a monotonically decreasing macroscopic density and pressure or a finite averaged macroscopic density and zero pressure in terms of the energy-momentum tensor for a perfect fluid. Therefore it violates the Principle of Equivalence and Special Relativity as required by Einstein himself for his gravitational field model. So not only is it Creationism, it's also schizo.

>>11746302
>>11746678
Your samefag falsefagging is painfully obvious to observe.

>>11746667
>They are repeating forever, meaning they never reach 1.
It's the number that is equal to 1, not a particular decimal. The number 0.999... always has infinite 9s, there is no timed process involved.

You are free to provide a proof or counter >>11746223 but so far you have failed.

>>11746771
>there is no timed process involved
Nobody has ever claimed that.

>>11746541
>the infinite amount of 9's is already there.
Indeed. And that means they it will never amount to 1. Just because they're infinite doesn't make it 1.

To word this differently, as it might help you understand better: 0.999 (three 9s) is less than 1. You know this. Okay. Now consider the following. Just because you have maaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaany * 9s after 0. doesn't mean it's the same as 1, either.

* so many that the 9s are infinite/endless

1 - 0.999... = ?

>>11746724
>>11746739
Attacking the source and not the idea itself is the lowest form of argument.

>Furthermore, the Big Bang creatio-ex-nihilo Creationism consists of a universe that's entirely filled by a continuous indivisible distribution of mass with a monotonically decreasing macroscopic density and pressure or a finite averaged macroscopic density and zero pressure in terms of the energy-momentum tensor for a perfect fluid.
Please explain how the Big Bang implies either of these.

>Therefore it violates the Principle of Equivalence and Special Relativity as required by Einstein himself for his gravitational field model.
How?

>>11746771
It's worthless because less than 1 isn't the same as 1, and no equation can ever change that. You can't use math to turn something non-existant or not real into something real. It will only be real in the equation, in the math, not in the real world in which we live. You can use math to "prove" anything, case in point: even schizo garbage like black holes, dark matter and creationism. Math is merely a tool. Like any tool, whether it's used correctly or for a good purpose is entirely up to the user of said tool.

>>11746724
>>11746739
https://www.youtube.com/watch?v=T9q-v4lBGuw

>>11746847
0.000...1

>>11746892
this is the part where you dumbfuck faggots fall apart.
You claim that other people are "incapable of grasping infinity/eternity" but then go on to claim that 0.000...1 makes any sense whatsoever. You can't have an infinite amount of zeros and then a one to terminate the string BECAUSE THEN THERE AREN'T AN INFINITE AMOUNT OF ZEROS YOU DUMB FUCK.

>>11746811
>Nobody has ever claimed that.
You have repeatedly:
>Just because the 9s are infinite doesn't mean they eventually reach 1.
>They never do.
>Eternally.
>They're forever approaching 1.
>They are repeating forever
>they never reach 1
>It will get very "close" to 1

It should be very simple for you to phrase your argument without referencing a process in time yet that's all you've done. You also failed to counter these proofs: >>11746223

>>11746770
im not falseflagging shit. cope harder and take your meds schizo. I just suddenly realised anon had a point, when I say 1/3 is 0,333... I actually mean its excactly that, 1/3, as in if you multiply it by 3 you dont get 1 - some really small number but you do in fact get a whole number. But that just made me think that we shouldn't say 1/3 = 0,333.. but that it's simply 1/3

>>11746847
It's 0.000... by the way, which is the same as 0. So 1 - 0.999... = 0

>>11746922
IF a - b = 0 then a = b

>>11746811
>And that means they it will never amount to 1.
Why? Also why do you keep saying "never" when time is not involved? You are just saying 0.999... is not 1. But you won't give a proof.

>Just because you have maaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaany * 9s after 0. doesn't mean it's the same as 1, either.
But infinite 9s does. Just because something is true for a finite amount of 9s doesn't mean it's true for an infinite amount of 9s. I leave you to your proof.

>>11746881
>less than 1
By how much exactly?

>>11746972
>666
get out with your satanic math, this is a christian thread

>>11746881
>It's worthless because less than 1 isn't the same as 1, and no equation can ever change that.
Where did i say less than 1 is the same as 1? You are just assuming 0.999... is less than 1 without proving it. Your argument is circular.

>You can't use math to turn something non-existant or not real into something real.
I didn't, I proved 0.999... = 1 by construction of the reals. You have no counter to the proof other than stating it contradicts your assumption, so you lose the argument.

>>11746892
The limit of the truncations of 0.000...1 is 0 so 0.000...1 = 0.

>>11746667
The finite decimals approach 1, not the infinite decimals. You're just confusing the infinite for the finite.

It's like saying 3.14... is less than pi because the decimal truncations only approach pi. But 3.14... is pi exactly.

>>11746881
>You can use math to "prove" anything
Then why have you failed to prove 0.999... is less than 1?

>>11746900
With 0 you can, as it's the only number which is both infinite and equivalent to nothing at the same time.

>>11747037
>0.000...1 = 0
False. "0.000...1" will always be close to 0, and never equal to 0. It's forever more than 0.

>>11747212
Doesn't follow.

>>11747136
not the one you replied to. you did reply earlier with your proof. I honestly don't understand your second proof when you start using ceiling log (because I dont know what this is). Its funny because I as a layman non-math, I wanted to use the 1-1/10^n thing to proof that 0.999... =/= 1. But somehow saying lim as n-> inf made me think of infinity more as a concept than an eternally long number maybe? Same as the 1/3 = 0.333....

I dont know anon.. it still feels weird of like theres something wrong with this reasoning.
Is there a way to describe the 'negative' space at the end? the infitely small part? Does this only work when you're at the last digit of your number system? Clearly 0.998... isn't 1 and neither would be 0.9999999999999998 (you always have to show all the numbers before you end the string)

>>11747250
>"0.000...1" will always be close to 0, and never equal to 0.
You claim this but I already proved they're equal by construction of the real numbers. You are free to find a flaw in the proof or present your own proof. Unproven claims will be ignored.

>>11747366
>I honestly don't understand your second proof when you start using ceiling log (because I dont know what this is).
The ceiling function ceiling(x) returns the smallest integer greater than or equal to x. So I'm just using it to find an integer n which is bigger than log(1/(1-x)).

>Does this only work when you're at the last digit of your number system?
There is no last digit. That's what makes it infinite.

>>11747448
i mean 9, in binary this would be 1

>>11745814
You're wrong but not because of>>11746012

0.333... -> 1/3
0.333... != 1/3

It approches 1/3 but it doesn't reach it.
Because 0.3333.... isn't a rational number, it can't actually be represented in reality, only in relation to other things. Therefore it will only ever approach 1/3 it will never actually by 1/3.
By this logic

0.999... -> 1
0.999... != 1

Shit is basic calculus, senpai.

>>11746243
Where were you when quantum faggots ree about needing alternate equations when defending string theory.

>>11749490
>I don't understand limits

1≠1
proof:
one can't equal one because one has three letters
qed.
>the absolute state of limit deniers

>>11749606
>I can't explain why you don't understand limits

>>11749490
>0.333... -> 1/3
This is gibberish.

>0.333... != 1/3
This is false.

>It approches 1/3 but it doesn't reach it.
What approaches it? Are you taking about a limit?

>Because 0.3333.... isn't a rational number, it can't actually be represented in reality, only in relation to other things.
It is a rational number and can be represented in reality. You just did.

>By this logic
That's not logic.

>>11749490
go to college

>>11749736
>0.333... != 1/3
This part is wrong, so
>By this logic
>0.999... != 1
uses bad logic to reach a worthless analogy

>>11749743
>are you talking about a limit
Yes.
In reality, there is no such thing as a decimal point - only proportional values. As such, decimal points are only ever approximations of reality.
Therefore, 0.333... effectively only ever approaches 1/3, it never actually reaches it.
This is why people, shortsightedly, use the term ~= to describe the relationship.
>This is gibberish
No, that's the sign for approaches.
If you think that's gibberish, you need to do what >>11749751 says.

>>11749754
Assuming without entertaining any alternate possibilities. The mark of a true scholar.

>>11749850
>Therefore, 0.333... effectively only ever approaches 1/3, it never actually reaches it.
A number doesn't approach anything, anon. Numbers are fixed. If you mean the values in the sequence (0.3, 0.33, 0.333, ...) approach 1/3 as your index grows, you would be right. And since 0.3... is defined as the supremum of the sequence, which is 1/3, this means 0.3... = 1/3.

>>11745814
Depends on what you're talking about.
1/3 of 3 cookies = 1 cookie
1/3 of 1 cookie = .333... Cookie

>>11749754
It's a definition, not an assumption.
We also define "one" as the English spelling equivalent of the number 1. But one has three letters, not one. Does this mean that every time someone writes out the word one it's not really the same as the number 1? How are you able to read any newspaper, for example, and not flip out?

>>11749873
>A number doesn't approach anything
Wrong. You are thinking of a value.
Decimal proportions are approximations of real proportions, not proportions themselves, as such, they are not values and are not truly fixed in reality.
This bass ackwards assertion of a duality of values is actually a fine example to demonstrate that it is.

x = 0.99...
10x = 9.99...
10x - x = 9x = 9
9x / 9 = x = 1
0.99... = 1
As simple as it gets

>>11749850
meant for you

>>11749925
What are your thoughts on Cantor's diagonal?

>>11749925
Do you mean that the string "0.9..." does not equal the string "1"? That's trivially true. But the mathematical objects we represent with these strings are the same. Both the supremum of the sequence (0.9, 0.99, 0.999, ...) and the value one are equal to 1.

>>11749850
>Yes.
The limit of what though? You realize that the limit doesn't "approach" anything right? It's the function or sequence which approaches the limit. So what function or sequence are you talking about?

>In reality, there is no such thing as a decimal point - only proportional values.
Why?

>Therefore, 0.333... effectively only ever approaches 1/3, it never actually reaches it.
Why?

>No, that's the sign for approaches.
Yes, that's why what you wrote is gibberish.

>>11749925
>Wrong. You are thinking of a value.
Numbers are values.

>Decimal proportions are approximations of real proportions
They aren't. If they are approximations then they aren't equal, but it's already proven they are: >>11746223