/sci/ - Science & Math

>acknowledging the truth makes one a moron
Anon, I...

>>11541285
>He still thinks you can reason with 0.999...==1 morons.

>>11541285
0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999...

>>11541285
>>11541319
...9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999...

>>11541285
>>11541322
...9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999...

>>11541285
>>11541319
>>11541322
>>11541324

WHERE'S THE FUCKING 1 YOU CRETINOUS MONGOLOIDS?

>>11541319
>>11541322
>>11541324
Unhinged.

>>11541319
>>11541322
>>11541324
-0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000...

>>11541331
...0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000...

>>11541332
...1 = 0

1/inf=0

>>11541285
you act like it's something you understand

you dont

shut the fuck up

>>11541327
Here.

>>11543198
The real numbers are not hard to understand. Neither is the simple definition of the real number represented by an infinite sequence of digits.
You seem angry.

if .999999 to infinity effectively 1 so is then 1.1111111111 effectively 1 also? Is this working with infinities averages.

Intuitionalism. Would suggest you can't haeve. .999999999 of dog to get 1 whole dog.

>>11543910
>1.1111111111 effectively 1 also
No. 1.111.... is exactly 10/9.

>>11543910
Intuitionalism suggests that if you have 0.9999.... dog, then you sure as hell have more than 0.9 dog, more than 0.99 dog, more than 0.999 dog etc. Intuitionalism then suggests you must have no less than 1 dog.

>>11543922
But that never becomes effectively 1 dog, at that point how do you decide rationally when it is effectively 1 dog?
I can't followed calculus argumentation.

>>11543924
>But that never becomes effectively 1 dog
what do you mean by "never becomes?"
0.999... dog is not an increasing amount of dog. it's a fixed amount of dog.

>>11541285
>3 thirds doesn't equal 1 according to sci brainlets

0^0=1...

>>11544051
Literally no one disagrees that 3 thirds equal 1, brainlet.

>>11544058
Yes and what is one third in decimals?

>>11544076
0.333....4

>>11544058
>>11544106
funny

>>11544076
Doesn't exist in decimals

>>11544139
so you accept only finite decimal expansions ?

>>11543910
>is then 1.1111111111 effectively 1
in base 2 it's exactly 10

>>11544154
An infinite expansion still isn't 1/3.

posting 0.999... threads should be punished with a ban for troll posting outside of /b/

>>11544196
prove it

>>11544196
every math text says otherwise
you're going to have to cough up a proof worthy of a Fields medal

>>11544216
>>11544218
This is what I find funny about /sci/.

You're trying to defend mathematical convention, but you don't even know what mathematical convention is.

No, in normal mathematics, a third does not exist as a decimal expansion, even infinite. HOWEVER, the LIMIT, of said decimal expansion, is a third.

Lmfao these are the brainlets arguing that 0.3333...=1. Can't even get basic highschool maths right.

>>11544310
>No, in normal mathematics, a third does not exist as a decimal expansion, even infinite. HOWEVER, the LIMIT, of said decimal expansion, is a third.

one and the same, retard
read a book

>>11544310
>No, in normal mathematics, a third does not exist as a decimal expansion, even infinite. HOWEVER, the LIMIT, of said decimal expansion, is a third.
so 0.333... is not a real number to you, but a sequence instead ?

>>11541327
ahem, I have an announcement to make

1/3=0.3333...
2/3=0.6666...
0.9999...=3/3=1

>>11544320
By the ellipsis definition, it's a non terminating sequence. Unless you believe that infinity has an end point. You don't actually believe that, right?

>>11544341
>By the ellipsis definition, it's a non terminating sequence.
So is every number: 2 = 2.000...

>>11544341
I believe that if you want to have a meaningful discussion about 1/3 = 0.333..., then both RHS and LHS need to be real numbers. you're saying that 0.333... is a sequence, otherwise you wouldn't be sepaking about its limit.

Wait so what does this mean? If I've bitten a chunk of banana, does that mean I am still holding a banana or have I eaten a banana?

>>11544344
That correct, yes.

Generally we have terminating conditions by the calculations required to achieve said number. By using (...) you are overriding those termination conditions.

>>11544354
(...) implies it is a sequence. Sequences can have limits. You must be 18 years of age to use this website.

>>11544354
You misunderstand. The notation .333... is not a sequence. It represents a limit which is a real number.

>>11544364
WRONG
>https://en.wikipedia.org/wiki/Decimal_representation#Recurring_decimal_representations
>The decimal expansion of a rational number is either finite, or endlessly repeating.

>>11544389
Thank you for confirming that you do not understand any of those words. However, do not hold your breath waiting for me to teach you.

>>11544363
>Generally we have terminating conditions by the calculations required to achieve said number. By using (...) you are overriding those termination conditions.
I can calculate 1/3 = 0.333... in only three steps. It's easy to get an infinitely repeating decimal with a finite calculation.

>(...) implies it is a sequence
No, it implies the decimal repeats without end.

All real numbers can be represented by sequences of numbers that converge towards a certain value. This is one way of constructing the real numbers. The decimal truncations of 0.999... and 1.000... are sequences that converge to the same number, 1. Therefore 0.999... and 1 are the same number.

Another way to construct real numbers is to divide the number line into two sets A and B such that every element of A is less than every element of B, and A has no greatest element. Since every number less than 0.999... is also less than 1, this means 0.999... and 1 are the same number.

>>11544412
Sweaty, just because two sequences converge to the same number doesn't mean they are the same number.

So much wrong with everything you've vomited up here.

>>11544412
*Since every number less than 1 is also less than 0.999..., this means 0.999... and 1 are the same number.

>>11544417
>Sweaty, just because two sequences converge to the same number doesn't mean they are the same number.
>the same number are not the same number
Please construct the real numbers such that this isn't true.

>>11544417
>So much wrong with everything
You are truly the guy from the internet, I tip my fedora.

>>11544428
Lim(0.9999)=1 however 0.9999... is not equal to one.

Welcome to highschool maths, sweaty.

>>11544417
>>11544363
you're mixing stuff up

an object is either a sequence of real numbers or a real number. not both.

if you think of 0.333... as the sequence (0.3,0.33,0.333,...), then 0.333... != 1/3 trivially, because they're not even an object of the same type.

the symbol 0.333... stands for the real number defined as the limit of this sequence. check wikipedia for fuck's sake

>You must be 18 years of age to use this website.
likewise

>>11544457
>check wikipedia for fuck's sake
Big yikes broseph

(...) doesn't mean limit, never has. Just because your s o y addled kin defaced the wiki doesn't mean it's true.

What is a number x, so that
0.99999... < x < 1?
There isn't one.
If you know your analysis, then this should be obvious: if there is no other real number between a and b, then a = b.
Confusion between the logic of the set N and R is one of the most common downfall of you dumb shits.
You all should have taken Analysis.

>>11544461
>(...) doesn't mean limit, never has.
cite one source where the ellipsis in decimal notation doesn't mean a limit or a supremum

>Just because your s o y addled kin defaced the wiki doesn't mean it's true
check the referenced real analysis books then

also you're retarded because you're literally saying that decimal expansions do not represent real numbers.

>>11544440
>Lim(0.9999)=1
No it is not. The limit of 0.9999 is 0.9999, which is less than 1.

>>11544440
>Lim(0.9999)=1
No, Lim(0.9999) = 0.9999

>however 0.9999... is not equal to one.
I already proved it does by construction of the reals. You have no counterargument, so you admit 0.999...=1. Thanks.

>>11544477
Axtually, there is no real number 0.9999. The true decimal expansion of 9999/10000 has to be written 0.9998999...

>>11544521
Clearly you are returdid if you think that 0.9999 = 0.999899989998...

>>11544477
>>11544479
Very funny TARDS, but I clearly meant to type ... after the 9.

0.9... has dot s dots mean more 9
1 not 9

>>11544531
So you are saying that the ... ellipses has some kind of meaning to you? Did you tell your parents about that, or do you keep it a secret to everyone what you think that its meaning might be?

Two proofs 0.999... = 1

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.

>>11544559
>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.

kek, are you retarded?

>>11544705
is something wrong, brainlet ?

>>11544719
If you cannot see it, I'm afraid you are terminal stupid.

First of all, you didn't not relate 0.9999.... past the initial inequality.

Second of all, your assigning of n has to abide by the previous inequality. If you think ceiling(log(1/(1-x)))+1 serves as an index for 0.999... (it doesn't) you need to explain so.

Basic stuff.

>>11541285
do you not believe in reason or something

>>11544780
>First of all, you didn't not relate 0.9999.... past the initial inequality.
irrelevant
>If you think ceiling(log(1/(1-x)))+1 serves as an index for 0.999... (it doesn't) you need to explain so.
the sequence is indexed by natural numbers. this is a natural number.

also I didn't write the post

>>11544802
That makes you double retarded, chum.

>>11541285
The geometric series explanation was the first one that made sense to me. Why don't we just show everyone that?

>>11544364
https://en.wikipedia.org/wiki/Repeating_decimal#Repeating_decimals_as_infinite_series

Nigga

>>11544457
>because they're not even an object of the same type
absolute retard

>>11544904
because schizos think that 0.999... is not the sum, they think "it's getting close to the sum but it never gets there" which doesn't even make sense in the first place.

>>11544889
>no argument
thanks for agreeing with 0.999... = 1 then. bye

fucking americunts can't count and have to pull imaginary numbers out of their asses to make sense of their own incoherent scribbles

Wikipedia has a whole fucking article on this you dumb cunts. Guess what they have to say...

https://en.wikipedia.org/wiki/0.999...'


>As part of Ed Dubinsky's APOS theory of mathematical learning, he and his collaborators (2005) propose that students who conceive of 0.999... as a finite, indeterminate string with an infinitely small distance from 1 have "not yet constructed a complete process conception of the infinite decimal". Other students who have a complete process conception of 0.999... may not yet be able to "encapsulate" that process into an "object conception", like the object conception they have of 1, and so they view the process 0.999... and the object 1 as incompatible. Dubinsky et al. also link this mental ability of encapsulation to viewing 13 as a number in its own right and to dealing with the set of natural numbers as a whole.

>>11544915
a sequence of real numbers is not a real number. what a surprise

>>11544310
>repeating numbers don't exist

>>11544780
>First of all, you didn't not relate 0.9999.... past the initial inequality.
So? If the resulting inequality doesn't hold then the initial inequality doesn't hold.

>Second of all, your assigning of n has to abide by the previous inequality.
No, the inequality must be true for all n in order for the initial assumption to work. Since it is not true for the n we choose, the initial assumption is false. Welcome to basic proofs.

> If you think ceiling(log(1/(1-x)))+1 serves as an index for 0.999...
I have no idea what that means or what it has to do with my proof.

>>11544950
>t. didn't read the fucking article
>t. lacking the self awareness to see why this was posted

>>11544950
>sequence of real numbers
mongoloid can't even comprehend BASIC and INTUITIVE ways of representing the reals like lmao.
>1/3 =/= .3*

>>11544937
>>11544950
>In mathematics, 0.999... (also written as 0.9, among other ways) denotes the repeating decimal consisting of infinitely many 9s after the decimal point (and one 0 before it). This repeating decimal represents the smallest number no less than every decimal number in the sequence (0.9, 0.99, 0.999, ...).[1] This number is equal to 1. In other words, "0.999..." and "1" represent the same number. There are many ways of showing this equality, from intuitive arguments to mathematically rigorous proofs.

>>11541319
>>11541322
>>11541324
Damn anon don't need three posts to type 1

>>11544985
where did you get the impression that I'm disputing this

Let 0.999..., as it be expanded, with ever expansion get closer to 1. And let it eventually get to X. So X must be equal to one, for if it is lesser, then in truth the expansion was not getting closer to 1, but to X.

This is the only way to reason the infinitely expanding decimal. It is not intuitive, and it is probably due to the improper idea that an infinite process can 'finish' that it seems so off, but it's the only logically consistent answer.

>>11545021
with every expansion getting closer*
for if it is unequal*

the truth of the matter is that we should keep decimal representation at a minimal. use whole numbers when you need to, and ratios when you need to, but keep the floating point shit down.

>>11545021
>Let 0.999..., as it be expanded
It's already expanded, and already equal to 1. If you can't tell the difference between some finite string of 9s and 0.999... then go back to elementary school.

>>11545032
i'm agreeing with you.
reading comprehension?

>>11545021
>It is not intuitive, and it is probably due to the improper idea that an infinite process can 'finish' that it seems so off, but it's the only logically consistent answer.
it's not intuitive only if you think of it as "result of an endless process", because that's obviously paradoxical. once you stop doing this, it stops being weird completely. there are other approaches.

>>11544918
Lmfaooo the SUM is not the LIMIT

LMFAOOOOOO

pic related is (you)

>>11544310
1/7 = 142857/10^6 + (7*10^6)^-1
= 0.142857 + (7*10^6)^-1
= 0.142857142857 + (7*10^12)^-1
= 0.142857142857142857 + (7*10^18)^-1
:
= 0.142857... + (7*10^inf)^-1
= 0.142857... + 1/inf
= 0.142857... + 0
= 0.142857...

>>11545118
>infinite sum is not the limit of partial sums
ok

>>11545224
0.9999... is a SUM but it's only the LIMIT that equals 1

RE TARD

>>11543910
>muh gibberish

>>11545274
>infinite sum
>not a limit
pick one and only one

>>11544310
>No, in normal mathematics, a third does not exist as a decimal expansion, even infinite.
Yes it does. The limit IS the number denoted by the decimal expansion, by DEFINITION. What else could the decimal expansion possibly denote?
https://en.wikipedia.org/wiki/Decimal_representation
>Both notations above are, by definition, the following limit of a sequence:
GET FUCKED YOU STUPID RETARD.

>>11544389
>or endlessly repeating
So like 0.999..., which is the rational number 1. Thanks for proving the point, fucktard.

>>11544389
https://en.wikipedia.org/wiki/Decimal_representation
>Both notations above are, by definition, the following LIMIT of a sequence:
Thanks for btfoing yourself once again.

>>11544440
>Lim(0.9999)=1

>>11544363
>(...) implies it is a sequence
Wrong.
https://en.wikipedia.org/wiki/Decimal_representation
>Both notations above are, by definition, the following LIMIT of a sequence:

>>11544440
>Lim(0.9999)=1
You don’t take the limit of a number you fucking RETARD. You take the limit of a sequence.

>>11541285
0.777... = 7/9
0.888... = 8/9
0.999... = 9/9 = 1

>>11545021
>Let 0.999..., as it be expanded
You can’t “expand” a number.

The end.

>>11545021
By the way I agree with you that 0.999... = 1, but you should reword this more carefully.

>>11545274
You can’t take the limit of a number, anon. You take the limit of a sequence, not a number. Why is this so difficult for you to understand?

>>11544139
So only 10-adic rationals have a decimal expansion?

Then your definition of "decimal expansion" (TM, retard edition) is stupid and useless. I'll stick with the standard one, thanks.

>>11545351
>You can’t take the limit of a number, anon.

Lim x->inf [ k ] = k

>You take the limit of a sequence

You take the limit of a series, brainlet.

>>11545344
>0.777... = 7/9
0.888... = 8/9
0.999... = uhh...I don't know...I DONT KNOW!!!!

>>11545391
>Lim x->inf [ k ] = k
lol okay
Lim x->inf [0.999...] = 0.999...
on the other hand, we have this post >>11544440
therefore 0.999... = 1

>>11545351
I never said 0.9999... was a number RETARD

DUMB DUMB DUMB

>>11544477
>>11544479
>>11545331
>>11545340
>>11545448
SHUT UP IDIOTS I MEANT LIM(0.999...) RETARDS THAT CAN'T UNDERSTAND SIMPLE TYPO

>>11545391
You're not taking the limit of a number. You're taking the limit of a sequence that yields that number everywhere.

>>11545391
>You take the limit of a series
No you don't. You take the limit of the SEQUENCE of partial sums corresponding to that series. The series is DEFINED to be equal to that limit.

>>11545618
It is a number. A decimal expansion denotes a number. Is this ungraspable to you?

>>11545646
No you idiot (..) denotes a SERIES

>>11545650
>>11545642
to be 100% fair, the word "series" and the symbol [math]\sum_{n=1}^{\infty}a_n[/math] can mean either the sequence of partial sums, or the limit when the sequence is convergent. it's assumed that the reader is not a complete retard and can distinguish between those two based on the context.

when the context is comparing the symbol with a real number, it always means the limit.

when the context is decimal expansions, it always means the limit.

>>11545684
>when the context is decimal expansions, it always means the limit.
read the wikipedia page you DUMB PIG

https://en.wikipedia.org/wiki/Repeating_decimal#Repeating_decimals_as_infinite_series

TARD TARD TARD

pic related is (YOU)

>>11545706
>https://en.wikipedia.org/wiki/Repeating_decimal#Repeating_decimals_as_infinite_series
quote: That is, a repeating decimal can be regarded as the sum of an infinite number of rational numbers.

see the word "sum"? well, let's see what does wikipedia have to say about this:

https://en.wikipedia.org/wiki/Series_(mathematics)

quote: ...the limit is called the sum of the series.

>>11545729
>regarded as the sum of an infinite number of rational numbers.
NOT THE SAME AS SUM OF A SERIES
SUM OF A SERIES IS NOT AN ADDITION OPERATION, INSTEAD A LIMIT OPERATION
FIRST QUOTE WAS CLEARLY REFERRING TO SUMMING (ADDING) NUMBERS TOGETHER INFINITELY

>>11545761
>NOT THE SAME AS SUM OF A SERIES
Series = operation of adding infinitely many quantities = sum of infinitely many quantities = limit of partial sums. It's all right there.

You lose.

>>11545785
INCORRECT

SUMMING AN INFINITE NUMBER OF TERMS IS NOT THE LIMIT

0.9999... IS NOT EQUAL TO ONE

ONLY THE LIMIT IS

>>11545761
>sum of a series
>sum of an infinite number of numbers
wait, you're saying that these are not the same thing ?

>>11545792
>SUMMING AN INFINITE NUMBER OF TERMS IS NOT THE LIMIT
Read the article, you're wrong and you lose.

>0.9999... IS NOT EQUAL TO ONE
See >>11544559

You don't even need to do any sums to prove this.

>>11545650
The value of the series IS a number (namely 1), dummy.

>>11545794
CORRECT
SEMANTIC SIMILARITY, TECHNICAL DIFFERENCE
>>11545803
YOU STUPID IDIOT THE PROOF YOU QUOTE IS EVEN WRONG, HOW COULD YOU BE SO IDIOTIC? PEOPLE OF YOUR KIND NEED TO BE SHOT HOW CAN YOU NOT SEE THE FLAWS OF THAT SHITTY PROOF? IT WOULD GET REJECTED ANYWHERE THAT ISN#T SCHIZO CENTRAL

OF COURSE THE LIMIT IS EQUAL TO ONE BUT THE SUM OF ALL THE DIGITS IS PROVABLY NOT EQUAL TO ONE YOU FUCKING RETARD SHUT THE FUCK UP FROM NOW ON YOU SILLY PATHETIC WORM

RETARDED

>>11545706
From the same page:
>0.9999999 ... = 9/9 = 1, since the repeating block is 9 (also a 1-digit block)
What do you have to say to that?

>>11545811
what is "sum of an infinite number of numbers" then ?
what is "sum of all the digits?"

>>11545811
https://en.wikipedia.org/wiki/Decimal_representation
>Both notations above are, by definition, the following LIMIT of a sequence

>>11545811
>YOU STUPID IDIOT THE PROOF YOU QUOTE IS EVEN WRONG
How?

>OF COURSE THE LIMIT IS EQUAL TO ONE BUT THE SUM OF ALL THE DIGITS IS PROVABLY NOT EQUAL TO ONE
I already showed you the sum is equal to 1. Then I showed you 0.999... = 1 without even needing to do any sums. You lost.

If you have a disproof then post it, I need a good laugh.

>>11545815
WRONG
WRITTEN BY CHARLATANS

>>11545828
Lol. I accept your defeat.

>>11545811
>this is the moment where you start writing only insults, no mathematics, and after three posts you stop responding, because you've already realized you've been wrong.
we all make mistakes anon

>>11545811
[math]\sum_{n=1}^\infty \frac{9}{10^n} = 1[/math]
End of story. You lost.

>>11545811
>FLAWS OF THAT SHITTY PROOF
also I'd like some flaws in the proof please. so far you've only quoted it and called it idiotic.

>>11545863

SEE

>>11544705
>>11544780

>>11545884
>SEE
>>11544705
This is not a flaw.

>>11544780
See >>11544955

>>11545884
but anon, this has been already disputed by several people independently

dude went full retard mode lol >>11545901

>>11545926
What an idiot.

>>11544323
But 1/3>0.(3)

>>11546522
No, 1/3 = 0.(3).

Does base 10 have rounding error problems?

How would we know unless we do ALL math in other base counting systems to compare the answers?

>>11546527
prove it

>>11546533

>>11544469

n is natural

what a number n such that 1 < x < 2?

there isn't one

therefore 1 = 2

>your logic

I love these threads

>>11546522
prove it

[math]0.9^a = 9^-a[/math]

>>11546762
>n is natural
>what a number n such that 1 < x < 2?
n can be any natural number, x = 1.5. what does n have to with anything?

>inb4 REEEEEEEEE

>>11547492
what

>>11547492
what

>>11547492
what

>>11546762

R is densely ordered

therefore every set needs to be densely ordered

>your logic

It may not be wise to feed the spammer but
at least read the fucking calculus book for freshman math major.
For example,Apostle explains this shit in the first 32 pages.

>>11541285
my math prof thrashes me to accept 0,999...=1
its not!

>>11549036
he gave me bad marks and was compliantly unfair cause of this 0,999...= not 1.
You can understand that if you think in therms of parables instead of numbers.

>>11549040
as soon as we approaching infinity we can ague that everything can happen. so the augment that 2 parallels meet in infinity is not valid in that sense that you can prof it.

>>11549046
eternity starts to dissolve all rules. no matter if you have an physical space or just numbers.

>>11543864
>first line of the "proof"
>redefining what "=" means
nice try. we arent buying your arcane logic

>>11546522
hmm lets see.....

0.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 hmm still not equal to 1/3... idiot

>>11541285
0.999 DOES NOT EQUAL 1

Only Maths Nazis say otherwise.

Once the HOLY WAR for a finite Universe has been won I can assure you the sinners will not go unpunished.
We will round up the Maths Nazis, put them on trial, and find them guilty. Imagine them attempting to explain away their heresy once they standing before ALMIGHTY GOD!

>>11549547
Agreed

[math] \displaystyle
1 = \frac {3}{3} = 3 \cdot \frac {1}{3} = 3 \cdot 0. \bar{3} = 0. \bar{9}
[/math]

>>11549547
Based and schizpoilled

>>11546548
[math]\sum_{n=1}^\infty \frac{3}{10^n} = \frac{1}{3}[/math]

>>11549547
>0.999 DOES NOT EQUAL 1
Nobody says it does.

>>11549868
illiterate & crazy

>>11541285
It's quite sad, really. Their brains can't grasp the fact that two expressions (say, 1 + 1 and 2) can denote the same number.

>>11541333