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help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:41:07
epsilon definition?
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1
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Simon
7348
Simon
false
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 19:41:10
yeees
1
0
161,888,429,980,778,500
Simon Petrikov
9097
Simon Petrikov
false
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 19:41:21
epsilon definition
1
0
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:41:24
Eventually your terms bunch up towards a value
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:41:30
is the intuitive idea
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:41:49
to which we "set how bunched up they are" by epsilon
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 19:42:23
can you tell me what every part means in the definition and how can i use it
1
0
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null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 19:42:30
i mean its sssssssso abstract
1
0
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205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:42:38
$\forall\varepsilon>0, \exists N\in\mathbb{N}$ st $n\geq N\implies\abs{a_n-L}<\varepsilon$
0
1
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null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
510,789,298,321,096,700
TeXit
01/29/2022 19:42:41
**Mosh**
https://cdn.discordapp.c…587366215691.png
186109587366215691.png
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:42:55
|a_n-L| is the distance b/w a_n and L
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:43:30
so you will hit a point in the index (N) such that all terms past it are within a distance epsilon away from L
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:43:38
for any distance epsilon
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 19:43:48
so epsilon is a distance
1
0
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:43:51
yes
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:44:11
your terms will eventually be less than epsilon away from L
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 19:44:35
can you give me an exmaple of a function
1
0
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null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 19:44:40
and keep subtituting
1
0
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 19:44:45
i can't imagine the idea
1
0
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null
null
null
null
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help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 19:44:46
i mean i can
1
0
161,888,429,980,778,500
Simon Petrikov
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Simon Petrikov
false
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 19:45:12
but yesterdya i was trying to do this exercice where you have to prove that 1/n is a cauchy sequence
1
0
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:45:38
Ok so yeah, cauchy criterion says that a_n is cauchy iff it's convergent
0
1
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null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:45:48
so we'll show 1/n converges (to 0)
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:46:30
Ie, we want to find N such that when $n\geq N$, we have that $\abs{\frac{1}{n}-0}<\varepsilon$
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
510,789,298,321,096,700
TeXit
01/29/2022 19:46:33
**Mosh**
https://cdn.discordapp.c…587366215691.png
186109587366215691.png
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 19:46:58
we don't have to fix epsilon at the start ?
1
0
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:47:10
You don't fix it persay
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:47:14
you just let it be given
0
1
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null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:48:09
So I'll leave it to you to 1) verify this N exists and 2) try and derive it yourself, however: \\ Let $\varepsilon>0$ be given. Pick N st $N>\frac{1}{\varepsilon}$
0
1
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null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
510,789,298,321,096,700
TeXit
01/29/2022 19:48:12
**Mosh**
https://cdn.discordapp.c…587366215691.png
186109587366215691.png
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:48:53
ie N is a natural number > 1/eps
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Momonα
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Momonα
false
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 19:49:46
that would be 1 > ?
1
0
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dldh06
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dldh06
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205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:49:58
So when $n\geq N$, we have that $n>\frac{1}{\varepsilon}\iff \frac{1}{n}<\varepsilon$
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
510,789,298,321,096,700
TeXit
01/29/2022 19:50:04
**Mosh**
https://cdn.discordapp.c…587366215691.png
186109587366215691.png
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:50:23
QED pretty much
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:50:40
N is defined/picked based on epsilon
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:50:48
It's just any natural number larger than 1/eps
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 19:51:05
that's what we mean by N depend on epsilon ?
1
0
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:51:13
Yes
0
1
898,472,021,061,685,200
thatsawesome
4282
thatsawesome
false
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:51:21
N is a "function" of epsilon
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:51:30
as in we define N based on epsilon
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:52:19
for example, let's say I want my terms to be within $\varepsilon=10^{-10}$ of 0
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
510,789,298,321,096,700
TeXit
01/29/2022 19:52:22
**Mosh**
https://cdn.discordapp.c…587366215691.png
186109587366215691.png
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:52:35
I then pick $N>10^{10}$
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
510,789,298,321,096,700
TeXit
01/29/2022 19:52:44
**Mosh**
https://cdn.discordapp.c…587366215691.png
186109587366215691.png
0
1
261,933,205,387,477,000
riemann
2529
riemann
false
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 19:54:02
hummmm one second to process this
1
0
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:54:30
then $a_{10^{10}+2}, a_{10^{10}+3},...$ are all within that $\varepsilon$ of 0
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
510,789,298,321,096,700
TeXit
01/29/2022 19:54:32
**Mosh**
https://cdn.discordapp.c…587366215691.png
186109587366215691.png
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 19:54:57
hum i never saw it this way
1
0
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 19:55:35
so we fix an arbitrary epsilon and then n after a certain N so that a_n is less than epsilon
1
0
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 19:55:52
i mean every n after that certain N
1
0
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:56:12
If I give you an epsilon, I want to know when I can guarantee the sequence will be within that distance from L
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
321,445,119,171,756,000
Shuri2060
01/29/2022 19:56:35
https://www.desmos.com/calculator/jn5jcxq3u0 We play a game. You will change the a slider. I will then change the N slider so all the dots to the right of N are in the shaded region. If I can always do this, it converges.
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:56:41
Your job is providing me with said N, then demonstrating said N works
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 19:57:21
i get the idea but the mathematic way of writing it is a bit confusing to me
1
0
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 19:58:22
"For any positive epsilon, then there exists natural number N defined by epsilon such that if I'm past N, I'm within epsilon of L"
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 19:59:36
okey that was a great way of stating it
1
0
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
186,109,587,366,215,680
Omegabet_
01/29/2022 20:00:14
I leave it to you to construct the similar "layman idea" for limits of functions Hint: delta also plays the role of a distance
0
1
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 20:01:10
i see your point
1
0
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 20:01:17
i have one last problem
1
0
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 20:02:38
okey nvm i forgot the question
1
0
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 20:02:42
thank you goood sir
1
0
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 20:03:48
thank you @Shuri2060 for the graph
1
0
null
null
null
null
null
205,746
help-1
3055db4fe95b4eed8fdd35e11f8e5b75
217,248,583,227,801,600
itsalivenger
01/29/2022 20:03:52
.close
1
0
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
165,315,789,044,318,200
baducca
01/29/2022 20:05:06
anyone know how to solve this?
https://cdn.discordapp.c…cb59d62effc4.png
7a03455f41ba9bff8fefcb59d62effc4.png
1
0
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
251,854,584,597,708,800
PapaBread
01/29/2022 20:07:03
Is this a calculus based class?
0
1
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
165,315,789,044,318,200
baducca
01/29/2022 20:07:11
Correct
1
0
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
251,854,584,597,708,800
PapaBread
01/29/2022 20:07:47
Do you know how to derivate it?
0
1
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
165,315,789,044,318,200
baducca
01/29/2022 20:07:57
I know more or less
1
0
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
165,315,789,044,318,200
baducca
01/29/2022 20:08:07
derivate meaning what tho?
1
0
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
165,315,789,044,318,200
baducca
01/29/2022 20:08:11
i know IROC
1
0
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
251,854,584,597,708,800
PapaBread
01/29/2022 20:08:42
To find the derivative
0
1
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
165,315,789,044,318,200
baducca
01/29/2022 20:08:59
all i want is how to solve B and C
1
0
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
165,315,789,044,318,200
baducca
01/29/2022 20:09:00
:(
1
0
null
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help-1
b4de5d36951848eb827f6b23c5e15088
165,315,789,044,318,200
baducca
01/29/2022 20:09:07
it's so frustrating rn
1
0
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
251,854,584,597,708,800
PapaBread
01/29/2022 20:09:31
You have to find the derivative I would think
0
1
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
251,854,584,597,708,800
PapaBread
01/29/2022 20:09:44
Do you know the power rule
0
1
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
200,013,547,491,688,450
a disappointing son
01/29/2022 20:10:08
is it derivate or differentiate
0
1
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
165,315,789,044,318,200
baducca
01/29/2022 20:10:35
I don't
1
0
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
165,315,789,044,318,200
baducca
01/29/2022 20:10:48
all i need is the IROC at x=2
1
0
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
251,854,584,597,708,800
PapaBread
01/29/2022 20:10:48
Differentiate prob
0
1
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
200,013,547,491,688,450
a disappointing son
01/29/2022 20:10:52
do you know the limit definition of a derivative?
0
1
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
165,315,789,044,318,200
baducca
01/29/2022 20:10:53
and x =3
1
0
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
251,854,584,597,708,800
PapaBread
01/29/2022 20:10:54
Couldnt think of the right term
0
1
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
165,315,789,044,318,200
baducca
01/29/2022 20:11:01
I dont
1
0
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
251,854,584,597,708,800
PapaBread
01/29/2022 20:11:09
How are you gonna find the iroc without the derivative though
0
1
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
165,315,789,044,318,200
baducca
01/29/2022 20:11:22
idek what that means im sorry
1
0
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
251,854,584,597,708,800
PapaBread
01/29/2022 20:11:37
Like
0
1
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
251,854,584,597,708,800
PapaBread
01/29/2022 20:11:39
d/dx?
0
1
265,853,506,664,136,700
ScapeProf
9427
ScapeProf
false
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
251,854,584,597,708,800
PapaBread
01/29/2022 20:11:44
f'(x)
0
1
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
165,315,789,044,318,200
baducca
01/29/2022 20:11:47
i didnt learn it that way
1
0
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
165,315,789,044,318,200
baducca
01/29/2022 20:11:49
i use f(x)
1
0
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
200,013,547,491,688,450
a disappointing son
01/29/2022 20:12:08
...you said this was a calc based course?
0
1
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
165,315,789,044,318,200
baducca
01/29/2022 20:12:26
yes
1
0
265,853,506,664,136,700
ScapeProf
9427
ScapeProf
false
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
165,315,789,044,318,200
baducca
01/29/2022 20:12:28
we just started
1
0
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
165,315,789,044,318,200
baducca
01/29/2022 20:12:32
rn its more algebra review
1
0
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
200,013,547,491,688,450
a disappointing son
01/29/2022 20:13:10
and you don't know limit definition?
0
1
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
165,315,789,044,318,200
baducca
01/29/2022 20:13:21
ik more or less
1
0
null
null
null
null
null
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
165,315,789,044,318,200
baducca
01/29/2022 20:13:23
do u know the answer or
1
0
189,360,428,298,666,000
shred
1973
shred
false
205,747
help-1
b4de5d36951848eb827f6b23c5e15088
165,315,789,044,318,200
baducca
01/29/2022 20:13:28
r u testing me
1
0
null
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