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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:21:14
??
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Kaisheng21
03/14/2022 15:21:30
i mean
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:21:33
you've found the taylor series
0
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:21:37
like you figured this out > (-1)^n * n!
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
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Kaisheng21
03/14/2022 15:21:37
you're done
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:21:48
like
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
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CoffeePls
03/14/2022 15:21:48
no i don't understand the process rn
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:22:05
https://cdn.discordapp.c…4640/unknown.png
unknown.png
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:22:08
so this is the end result
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1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:22:12
this is still a series
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209,767,680,100,663,300
Kaisheng21
4584
Kaisheng21
false
1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:22:17
the end result is a series
0
1
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null
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null
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1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:22:41
you're not finding an answer that doesn't have a sigma in it
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1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:23:46
like, there isn't gonna be any nice answer to 'what does this series of numbers equal'
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
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Kaisheng21
03/14/2022 15:23:58
there's not gonna be a more nice form than this last series
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
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CoffeePls
03/14/2022 15:24:28
https://cdn.discordapp.c…80274/image0.jpg
image0.jpg
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
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CoffeePls
03/14/2022 15:24:40
I guess my question is how the dude on the left became the dude on the right
1
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
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CoffeePls
03/14/2022 15:26:36
I don't follow how the blue line happened
https://cdn.discordapp.c…4912/unknown.png
unknown.png
1
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
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CoffeePls
03/14/2022 15:26:57
How are you able to just come up with an algebraic form like that
1
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:29:46
ok well if you ignore the minus signs
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:29:52
then it's just 1, 1, 2!, 3!, 4!
0
1
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1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:30:02
so it's just gonna be n!, right
0
1
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1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:30:08
now, considering the minus signs
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:30:17
it goes like +, -, +, -, +...
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:30:24
so that's gonna be (-1)^n
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
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CoffeePls
03/14/2022 15:30:30
right
1
0
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:30:32
oh wait
1
0
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
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CoffeePls
03/14/2022 15:30:35
how did u know to add ^n
1
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
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Kaisheng21
03/14/2022 15:30:38
because (-1)^0 = 1, positive
0
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
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CoffeePls
03/14/2022 15:30:38
I get the -1 part
1
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:30:42
(-1)^1 = -1, negative
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:30:42
but why ^n?
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:30:52
(-1)^2 = 1, positive
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:30:57
(-1)^3 = -1, negative
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:30:57
ohhh
1
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d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:31:00
OH WOW
1
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d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:31:01
ok
1
0
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:31:03
so yeah it's just a thing that works
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:31:06
right
1
0
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:31:19
this is why I get hooked on calc
1
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:31:21
:feelsbadman:
1
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:31:43
the dopamine kick I just got from figuring out (-1)^n is better than ~~cocaine~~ caffeine
1
0
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:32:03
What about n!?
1
0
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:32:10
Who says that's true for all n?
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:32:22
they just took it for granted bc the pattern is so obvious
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:32:27
they just assumed
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:32:32
you can probs prove it explicitly
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:32:41
induction
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1
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:32:43
Right but I'm a noob so I don't understand why it's taken for granted
1
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:32:53
like, I wouldn't be able to figure this out on an exam
1
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:32:54
well it's taken for granted bc it fits lol
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:32:55
:sadge:
1
0
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:33:03
because the 0th one is 0!
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1
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1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:33:06
the 1st one is 1!
0
1
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1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:33:10
the 2nd one is 2!
0
1
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1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:33:15
the 3rd one is 3!
0
1
null
null
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null
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1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:33:27
so they just assume it's gonna be like that always
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1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:33:35
https://cdn.discordapp.c…0324/unknown.png
unknown.png
1
0
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:33:39
because of the numerator?
1
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:35:03
yes
0
1
209,767,680,100,663,300
Kaisheng21
4584
Kaisheng21
false
1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:35:11
they just evaluate those at 1
0
1
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1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
209,767,680,100,663,300
Kaisheng21
03/14/2022 15:35:42
they put 1 in, and it comes out as 0! -1! 2! -3! 4! so they just assume it's gonna be (-1)^n * n! the whole time
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:37:07
ohh
1
0
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:37:13
hm alright
1
0
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1,245
help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:37:17
im gonna go give this a try
1
0
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:37:20
thanks
1
0
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:37:27
@Kaisheng21ty
1
0
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help-10
d9f30e0c0c9445b78184e2c117d5db7e
852,592,874,754,932,700
CoffeePls
03/14/2022 15:37:29
.close
1
0
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help-10
39a1820286564eecbe63ed29d928e291
714,940,112,324,001,900
goodguyneo
03/14/2022 15:52:16
sin(180-2x) times 7.5 = 9 times sin (x)
1
0
null
null
null
null
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1,246
help-10
39a1820286564eecbe63ed29d928e291
714,940,112,324,001,900
goodguyneo
03/14/2022 15:52:26
how would i solve that?
1
0
null
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help-10
a5732c7cef724859897afa4f043ebe3b
221,261,455,893,200,900
FᴀʟʟᴇɴPɪᴀɴᴏ
11/09/2021 07:10:04
https://cdn.discordapp.c…3732/unknown.png
unknown.png
1
0
null
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null
null
null
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help-10
a5732c7cef724859897afa4f043ebe3b
221,261,455,893,200,900
FᴀʟʟᴇɴPɪᴀɴᴏ
11/09/2021 07:10:17
So here, I am given this, and is asked to demonstrate whether it is a subspace
1
0
null
null
null
null
null
1,247
help-10
a5732c7cef724859897afa4f043ebe3b
221,261,455,893,200,900
FᴀʟʟᴇɴPɪᴀɴᴏ
11/09/2021 07:11:01
Here, I am seeing if it is closed under addition, which I've shown that it is not with the work above
1
0
null
null
null
null
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1,247
help-10
a5732c7cef724859897afa4f043ebe3b
221,261,455,893,200,900
FᴀʟʟᴇɴPɪᴀɴᴏ
11/09/2021 07:11:29
Is the way I approached this proper and sufficient to say that it is not closed?
1
0
null
null
null
null
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1,247
help-10
a5732c7cef724859897afa4f043ebe3b
244,755,340,653,101,060
axis
11/09/2021 07:12:44
subspace of what?
0
1
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help-10
a5732c7cef724859897afa4f043ebe3b
221,261,455,893,200,900
FᴀʟʟᴇɴPɪᴀɴᴏ
11/09/2021 07:13:52
I don't know how to answer that question, can you clarify?
1
0
null
null
null
null
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1,247
help-10
a5732c7cef724859897afa4f043ebe3b
221,261,455,893,200,900
FᴀʟʟᴇɴPɪᴀɴᴏ
11/09/2021 07:14:05
This is all I was given
https://cdn.discordapp.c…9259/unknown.png
unknown.png
1
0
null
null
null
null
null
1,247
help-10
a5732c7cef724859897afa4f043ebe3b
244,755,340,653,101,060
axis
11/09/2021 07:14:32
subspaces of R, then?
0
1
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null
null
null
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1,247
help-10
a5732c7cef724859897afa4f043ebe3b
221,261,455,893,200,900
FᴀʟʟᴇɴPɪᴀɴᴏ
11/09/2021 07:14:40
That sounds right
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help-10
a5732c7cef724859897afa4f043ebe3b
244,755,340,653,101,060
axis
11/09/2021 07:15:58
welll, if it fails to be closed under addition, it's not a subspace
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help-10
a5732c7cef724859897afa4f043ebe3b
221,261,455,893,200,900
FᴀʟʟᴇɴPɪᴀɴᴏ
11/09/2021 07:16:14
Right
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help-10
a5732c7cef724859897afa4f043ebe3b
244,755,340,653,101,060
axis
11/09/2021 07:16:24
assuming the addition is that associated with R
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help-10
a5732c7cef724859897afa4f043ebe3b
244,755,340,653,101,060
axis
11/09/2021 07:17:13
there is an extra +1, so...
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help-10
a5732c7cef724859897afa4f043ebe3b
221,261,455,893,200,900
FᴀʟʟᴇɴPɪᴀɴᴏ
11/09/2021 07:17:47
So what I've written up there is correct and sufficient to conclude that it is not a subspace?
1
0
209,767,680,100,663,300
Kaisheng21
4584
Kaisheng21
false
1,247
help-10
a5732c7cef724859897afa4f043ebe3b
244,755,340,653,101,060
axis
11/09/2021 07:17:57
and the condition being that the second entry = 1st entry + 3rd entry + 1
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help-10
a5732c7cef724859897afa4f043ebe3b
244,755,340,653,101,060
axis
11/09/2021 07:18:00
sure
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help-10
a5732c7cef724859897afa4f043ebe3b
244,755,340,653,101,060
axis
11/09/2021 07:18:45
you'd probably have to say that the sum is not equivalent to the one in the initial condition, though
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1,247
help-10
a5732c7cef724859897afa4f043ebe3b
221,261,455,893,200,900
FᴀʟʟᴇɴPɪᴀɴᴏ
11/09/2021 07:19:29
Yeah, you're right. It would be better to refer back to *"and the condition being that the second entry = 1st entry + 3rd entry + 1"*
1
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null
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help-10
a5732c7cef724859897afa4f043ebe3b
244,755,340,653,101,060
axis
11/09/2021 07:20:00
say that explicitly, then you're good
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1
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help-10
a5732c7cef724859897afa4f043ebe3b
221,261,455,893,200,900
FᴀʟʟᴇɴPɪᴀɴᴏ
11/09/2021 07:20:49
Thinking about it, that last statement is probably pretty important because what I've written up there doesn't tie to it not being a subspace if I don't state that
1
0
null
null
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1,247
help-10
a5732c7cef724859897afa4f043ebe3b
244,755,340,653,101,060
axis
11/09/2021 07:21:10
it also fails to be closed under multiplication by scalars
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help-10
a5732c7cef724859897afa4f043ebe3b
244,755,340,653,101,060
axis
11/09/2021 07:21:35
which might be more brief for you
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help-10
a5732c7cef724859897afa4f043ebe3b
221,261,455,893,200,900
FᴀʟʟᴇɴPɪᴀɴᴏ
11/09/2021 07:22:05
Oh I didn't consider that, thank you
1
0
null
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help-10
a5732c7cef724859897afa4f043ebe3b
221,261,455,893,200,900
FᴀʟʟᴇɴPɪᴀɴᴏ
11/09/2021 07:22:28
Alright, this was very helpful, I thank you for your time and response
1
0
null
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help-10
a5732c7cef724859897afa4f043ebe3b
221,261,455,893,200,900
FᴀʟʟᴇɴPɪᴀɴᴏ
11/09/2021 07:22:32
.close
1
0
null
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help-10
b7bdbf2332cc4d85901627861fb81d60
580,777,949,851,287,600
VnJ
03/14/2022 16:28:24
https://cdn.discordapp.c…_at_20.27.40.png
Screenshot_2022-03-14_at_20.27.40.png
1
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help-10
b7bdbf2332cc4d85901627861fb81d60
580,777,949,851,287,600
VnJ
03/14/2022 16:30:11
i got up to:
1
0
null
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help-10
b7bdbf2332cc4d85901627861fb81d60
580,777,949,851,287,600
VnJ
03/14/2022 16:30:27
2^2x - 18^x = -8
1
0
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help-10
b7bdbf2332cc4d85901627861fb81d60
580,777,949,851,287,600
VnJ
03/14/2022 16:33:17
wait im stupid its just a quadratic nvm
1
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help-10
b7bdbf2332cc4d85901627861fb81d60
580,777,949,851,287,600
VnJ
03/14/2022 16:33:22
sorry
1
0
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help-10
b7bdbf2332cc4d85901627861fb81d60
580,777,949,851,287,600
VnJ
03/14/2022 16:33:27
.close
1
0
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null