/sci/ - Science & Math

[Anonymous No.11804845]

Its time to throw this garbage meme in the trash
>B-BUT ITS INFINITESIMALLY DIFFERENT SO ITS THE SAME!!
NO, this is called ROUNDING, but they are literally not the same number. If they are then that means numbers arent real when they are.
Might as well accept that there just isnt a proper way to represent fractions like these as numbers, at all.

[Anonymous No.11804860]

>>11804845
>accept that there just isnt a proper way to represent fractions like these as numbers, at all.
Just use a different base. Why is this entire board so stupid?

[Anonymous No.11804889]

>>11804845
1/3 =0.3333...
0.3333...*3 = 0.99999....
1/3*3= 1
ergo 0.999...=1

[Anonymous No.11804892]

I truly can't understand why some people are incapable of understanding why .9999... is exactly equal to 1.
It all comes down to the sniveling dumbfuck retards thinking that 0.000....1 is a real thing. IF you don't immediately see why 0.000...1 doesn't make any sense, you're a retard.

[Anonymous No.11804905]

>>11804892
>It all comes down to the sniveling dumbfuck retards thinking that 0.000....1 is a real thing.
OP is a different kind of retard. he thinks that 0.999... = 1 means that if you round 0.999..9 you get 1.

[Anonymous No.11804907]

>>11804889
Faulty logic. Again, you rounded. You're mixing fraction logic with decimal logic.
>>11804892
Why would a number that is bigger than all other numbers above 0 make sense, but a number that is smaller than all numbers above 0 not? Whats next, 0.000...2 isnt real either cause it hurts your feefees?

You've been LIED TO. You can do nothing more than regurgitate what you have been fed. You would've believed the earth is flat when that was common

[Anonymous No.11804911]

>>11804845
I don't understand this image.

[Anonymous No.11804919]

>>11804907
I didn't round anything.
Where did i round any value?

[Anonymous No.11804920]

>>11804907
>Why would a number that is bigger than all other numbers above 0 make sense
it doesn't
>but a number that is smaller than all numbers above 0 not?
also doesn't
>Whats next, 0.000...2 isnt real either cause it hurts your feefees?
it isn't real because it's not a limit of a sequence of rational numbers

[Anonymous No.11804926]

>>11804905
I think what he's trying to get at is that its just an issue with decimal notation.
No one argues that three thirds equals one, only that when you try to put it into decimal notation that it looks goofy and leads to these cancerous low IQ threads.

[Anonymous No.11804929]

>>11804907
Go back to your mud hut

[Anonymous No.11804933]

>>11804907
Sniveling dumbfuck retard detected.
You can't have an infinite string of digits and then a digit to terminate the string because that is a contradiction - infinite doesn't terminate.
I was not "taught this" I understood this intuitively since I was like 7 years old. It is not a difficult thing to understand whatsoever.

Again, if you are not immediately able to see why 0.000...1 doesn't make sense (where the string of zeros are claimed to be infinite in length), you are a retard. If you claim that it's not an infinite string of zeros but just a very large finite amount and we use the ... because we can't write it all down, then that's not the same as 0.999... which is infinite, in which case (1 - 0.000...1) is strictly less than .999...

[Anonymous No.11804943]

>>11804920
>it doesn't
There you go, 1tards just said infinity doesn't make sense because IM TWIGGEWED MOOOOMMMYYYYYY
>it isn't real because it's not a limit of a sequence of rational numbers
Except there are infinitely many numbers, so you have no proof it isn't real.

[Anonymous No.11804950]

>>11804943
>Except there are infinitely many numbers, so you have no proof it isn't real.
False

[Anonymous No.11804952]

>>11804845
what number is there between 0.999... and 1?

[Anonymous No.11804953]

...sage...

[Anonymous No.11804957]

>>11804845
The first proof is wrong, here's why

>x = 0.33333.....
>10x = 3.3333......
>10x = 3 + 0.3333.....
>10x = 3 + x
>9x = 3
>x = 3

The second proof is also wrong, because you have a = b^2 and then ab = b^2, but it should be ab = b^3.

>>11804889
Wrong, that's like saying 2 * 3 = 6 and 5 * 3 = 15 so 2 = 5 and 6 = 15.

>>11804952
(1 + 0.999999...) / 2 and at least 5 more real numbers

[Anonymous No.11804958]

>>11804943
>There you go, 1tards just said infinity doesn't make sense because IM TWIGGEWED MOOOOMMMYYYYYY
nobody said that. practice your reading comprehension

[Anonymous No.11804959]

btfo

[Anonymous No.11804963]

>>11804933
>infinite doesn't terminate.
But it does keep going. No matter what positive number you have, 0.000...1 is smaller. Just like infinity is always bigger. Therefore 0.999... is always smaller than 1.

[Anonymous No.11804964]

>>11804959

[Anonymous No.11804966]

>>11804957
>x=3
wrong x=3/9 = 1/3

[Anonymous No.11804967]

>>11804933
>You can't have an infinite string of digits and then a digit to terminate the string because that is a contradiction - infinite doesn't terminate.
this is not really true. you can order "infinity" into an infinite string followed by a single element. it's just that an infinite set of digits ordered this way doesn't represent a real number.

[Anonymous No.11804969]

>>11804950
No please, explain how there arent infinitely many numbers. Name the maximum amount of decimal places a number can have, lets hear it.

[Anonymous No.11804970]

>>11804892
It seems fairly obvious that it is bait

[Anonymous No.11804974]

>>11804966
wrong 9/3 = 3

[Anonymous No.11804975]

>>11804969
There being an infinite amount of numbers (which there are) does not imply that there exists any such number.
0.0000...1 does not exist in the reals despite there being an infinite amount of unique real numbers.

[Anonymous No.11804977]

>>11804974

[Anonymous No.11804981]

Reminder that 1tards actually use arguments like
>YEAH IF YOU HAD AN APPLE AND TOOK AWAY A SINGLE ATOM ITS BASICALLY THE SAME
When no, it wouldnt be, it would have factually changed.

[Anonymous No.11804982]

>>11804957
>(1 + 0.999999...) / 2 and at least 5 more real numbers
that's like saying that 2 and 2 are different numbers because the number between them is (2+2)/2, it proves nothing. mind listing out these 5 other real numbers?

[Anonymous No.11804984]

>>11804957
>>9x = 3
>>x = 3
You're an actual fucking retard

[Anonymous No.11804985]

>>11804975
And yet infinity exists, right?

[Anonymous No.11804987]

>>11804982
Retard, you're assuming that 0.9999.... = 1 to make that argument, which is circular reasoning.

[Anonymous No.11804990]

>>11804845
Define 0.999...

[Anonymous No.11804992]

>>11804963
>Just like infinity is always bigger
Infinity is not a number
>>11804985
Infinity is not a number

[Anonymous No.11804994]

>>11804987
nope, he's just saying that an argument doesn't work (and he's right)

[Anonymous No.11804998]

>>11804987
I assumed no such thing? read it again :/

[Anonymous No.11805009]

>>11804992
If there are infinitely many numbers, then numbers have infinite decimal places, which means there are numbers that are always bigger/smaller than other numbers because thats how numbers are defined.

Tell me, if 0.333... exists, why wouldnt 0.333...4 also exist, the number right after it that is bigger than it? Why wouldnt 0.333...2 exist?

[Anonymous No.11805013]

>>11804998
>that's like saying 2 and 2 are different numbers
You're implicitly saying my argument doesn't work because 1 is actually 0.999999.... That's circular reasoning

[Anonymous No.11805016]

Is there any complex number between 0.9 periodic +0.9 periodic * i and 1+1i ?
If so, the distance between the two must be strictly higher than 0

[Anonymous No.11805017]

>>11804981
An atom is finite, not infitesimal.

[Anonymous No.11805022]

>>11805009
Because those last two numbers are finite but with an arbitrarily large number of 3's, retard.

0.333... != 0.333...3

[Anonymous No.11805026]

>>11805009
>because thats how numbers are defined.
nope
>Tell me, if 0.333... exists, why wouldnt 0.333...4 also exist, the number right after it that is bigger than it? Why wouldnt 0.333...2 exist?
every real number is the limit of a sequence of rational numbers. I can give you a sequence of rational numbers representing 0.333..., can you give me a sequence of rational numbers representing 0.333..4 ?

[Anonymous No.11805029]

>>11805009
>If there are infinitely many numbers, then numbers have infinite decimal places, which means there are numbers that are always bigger/smaller than other numbers because thats how numbers are defined.
False.
There are an infinite amount of unique real numbers and unique rational numbers between 0 and 1 but you will never find the real number pi in that open interval.
Just because there exists an infinite amount of unique things does not mean there exists any specific unique thing.
0.00...1 does not exist in the reals anywhere. Neither does 0.333...4 nor 0.333...2. This is obvious to anyone who isn't a retard.

[Anonymous No.11805031]

>>11805013
no, he's implicitly saying that your argument is not a priori wrong, it's incomplete. you need to prove that (1-0.999...)/2 is strictly bigger than 0.999... and strictly smaller than 1. do it please if you can

[Anonymous No.11805037]

>>11805013
your argument wouldn't work even if 0.999... and 1 weren't equal, dummy!

[Anonymous No.11805039]

>>11805031
>(1-0.999...)/2
should be (1+0.999...)/2 of course

[Anonymous No.11805040]

>>11805022
>0.333... != 0.333...3
They are exactly the same. It ends at infinity places, thats what repeating means.

[Anonymous No.11805049]

>>11805040
No they're not.
0.333... is infinite, and does not terminate. It's turtles all the way down.

0.333...3 is finite but arbitrarily large, because it terminates. It's an absurd number of turtles, infinite for all practical purposes, you couldn't hope to count them all in a billion universe-spans, but it's still finite.

[Anonymous No.11805053]

>>11804957
>>10x = 3 + x
>>9x = 3

9x/9 = 3/9
x = 3/9
3x = 9/9

[Anonymous No.11805054]

>>11805029
>0.00...1 does not exist in the reals anywhere.
You STILL havent explained why. Go back to >>11804907 and dilate

[Anonymous No.11805058]

>>11805049
>0.333...3 is finite but arbitrarily large, because it terminates
is this nigga for real ?

[Anonymous No.11805061]

>>11805049
>does not terminate.
But no matter what, its last digit is 3.

[Anonymous No.11805062]

>>11804957
>9x = 3
>x = 3
niggers were a mistake

[Anonymous No.11805063]

>>11805054
read >>11805026

[Anonymous No.11805076]

>>11805054
>You STILL havent explained why.
Yes I have. It is a contradiction to say there is an infinite amount of digits but then a last digit. This is a contradiction, therefore it is PROVEN wrong.

[Anonymous No.11805082]

>>11805058
Yes, smoothbrain.

>>11805061
There is no "last digit" in an infinite sequence. By it's own definition, a last digit implies termination of the sequence, and it is thus finite.

You can certainly have an infinite sequence of 3's, but there's no last digit.

[Anonymous No.11805092]

>>11805049
>0.333...3 is finite but arbitrarily large
0.333...3 is not a correctly expressed number
If you want to express it as a number, fucking do so.
[math]\sum_{i=1}^{n} \frac{3}{10^i}[/math] is an acceptable number, it is finite and you can easily write it as such, given any positive integer n larger than 1. That is what you're trying to express, fucking use your brain and whatever you fucking learned in high school

[Anonymous No.11805099]

>>11805082
>You can certainly have an infinite sequence of 3's, but there's no last digit.
And yet it will always be bigger than any finite sequence of 0.333 because no matter how long it is, 0.333... is bigger. Its last digit is the infinite-th digit, thats what infinity means. How are 1cucks this retarded?

[Anonymous No.11805103]

>>11805099
no such thing as infinite-th digit.

[Anonymous No.11805105]

>>11805092
I know how to use sigma notation, anon; how about you say that to the smooth brain pretending that it's infinite? I'm just using his terminology to try and get across his thick skull.

[Anonymous No.11805111]

>>11805099
>Its last digit is the infinite-th digit, thats what infinity means
No it doesnt, dummy

[Anonymous No.11805117]

>>11805063
>ME DEFINE LE RULES ME RIGHT
Numbers are numbers, they are defined by existing. There are infinite digits in everything because there is no cap. 0.333... has infinite digits because it does, not for any other reason.

[Anonymous No.11805127]

>>11805099
>Its last digit is the infinite-th digit
periodic notation implies that it cannot have a last digit, much like there's no "largest positive integer" because for any finite n, exists n+1 that is both larger and finite. The same applies here, there is always a more accurate approximation of the fraction that is one additional digit more accurate than the one you select.

[Anonymous No.11805128]

>>11805117
Troll

[Anonymous No.11805130]

>>11805103
So infinity makes no sense, and now infinitesimals make no sense? Your entire argument is predicated on the idea that infinitesimals arent real when... they are, theres no dispute there.

[Anonymous No.11805142]

>>11805099
And this is exactly what I was referring to in my first post here >>11804892
It comes from an inability to understand how infinity works.
The line "Its last digit is the infinite-th digit, thats what infinity means. How are 1cucks this retarded?" makes me think you're trolling and not serious because this is so fucking retarded I can't believe someone is seriously posting it.

[Anonymous No.11805148]

>>11805142
Infinitesimals are real, what did you think 0.000...1 was? Thats what it means.
>1cuck cant get a gf: "WOMEN ARENT REAL"

[Anonymous No.11805149]

>>11804845
have you actually studied mathematics? do you know what it means to write ".999...". If you haven't studied mathematics is it quite a complicated object to try wrap your head around what is meant.

without training it makes sense that two things that look different should be different

you could try and define numbers in such a way that 1-.9999...= infinitesimal. but you would not gain anything, and alot would be made much more complicated

[Anonymous No.11805157]

>>11805148
Whats 10*0.00....1?

[Anonymous No.11805160]

>>11805130
infinity makes perfect sense. infinite-th digit does not.
infinitesimals make perfect. but not in the field of real numbers.

[Anonymous No.11805163]

>>11805157
10*0.000...1.
>OH MY GOOOOOOOOD I CANT HECKIN WRITE THIS DOWN IT MAKES NO SEEEEEENSE
Up next on 1cuck radio "PI DOESNT EXIST". Hey that makes a good one: whats 10*pi?

[Anonymous No.11805165]

>>11805148
>Infinitesimals are real
False, infinitesimals are not real numbers
>what did you think 0.000...1 was?
A string of digits that you typed out that do not correspond to any real number. It's a semantically meaningless string of numbers that do not mean anything at all and do not represent any number that exists on the real line. You certainly can not use them as any sort of argument.
>Thats what it means.
It means nothing.
>>1cuck cant get a gf
false

[Anonymous No.11805171]

>>11805160
>infinity makes perfect sense
But you said it didnt, what happened? >>11804920

[Anonymous No.11805173]

>>11805149
I should note that this would be much different than the common notion of an infinitesimal

The problem here is that real numbers are quite abstract, we are only really comfortable with fractions. The decimal system is only a way of *representing* real numbers. The decimal system is intuitive when we only deal with numbers that have finite decimal representations, this is because these numbers are precisely the fractions. When we deal with numbers that have infinite decimal expansions things can get weird. I

f you work through how the real numbers are constructed you will come across the fact that the decimal representation of a number need not be unique, and hence why 1 and .999.. represent the same number.

[Anonymous No.11805176]

Why the FUCK ARE YOU FUCKING MORONS POSTING ON THE MATH BOARD WITHOUT EVEN KNOWING THE DEFINITION OF THE REAL FUCKING NUMBERS???
If you use dedekind cuts or equivalence classes of cauchy sequences of rationals, the DEFINITIONS of the reals, under these DEFINITIONS it is IMMEDIATELY OBVIOUS that 0.9999... and 1 are decimal expansions which ALWAYS refer to the EXACT same object.

[Anonymous No.11805177]

>>11805171
I never said infinity doesn't make sense. I said a *number* bigger than all numbers above 0 doesn't make sense. practice your reading comprehension.

[Anonymous No.11805179]

>>11805148
>>11805157
>>11805163
Not a fucking number
Use the fucking correct notation to express your fucking numbers
1.0E-91715 is a valid fucking notation to express a number, 0.000...1 is NOT