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help-1
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HeadShotCem
01/28/2022 07:05:24
I really am lmao
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help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 07:05:35
if two lines are perpendicular
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help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 07:05:45
the product of their lines is equal to -1
0
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help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 07:05:51
but if two lines are parallel
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help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 07:05:52
lool
1
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help-1
5c401f58b5854f3c8036a2204e3dcecf
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HeadShotCem
01/28/2022 07:06:00
their slopes must be equal
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Somalian Space Pirate
8980
Somalian Space Pirate
false
205,700
help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 07:06:07
and c1 != c2
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help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 07:06:14
Thats why I was saying this!
1
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5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 07:06:16
And then I got confused
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5c401f58b5854f3c8036a2204e3dcecf
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HeadShotCem
01/28/2022 07:06:27
yeah dude, I’m sorryy
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5c401f58b5854f3c8036a2204e3dcecf
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Deleted User
01/28/2022 07:06:29
🤦‍♂️
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help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 07:06:31
All good
1
0
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help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 07:06:39
But
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help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 07:06:41
c1 = c2
1
0
null
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help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 07:06:56
(-3/3) = (-3-2)/5
1
0
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help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 07:07:02
-1 = -1
1
0
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help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 07:07:07
So therefore m=3
1
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help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 07:07:30
wait, hmm
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5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 07:08:10
for the lines (a1)x+(b1)y+(c1)=0 and (a2)x+(b2)y+(c2)=0: (1) if they’re the same line, then a1/a2=b1/b2=c1/c2 (1) if they’re parallel, then a1/a2=b1/b2 but != c1/c2
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help-1
5c401f58b5854f3c8036a2204e3dcecf
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Deleted User
01/28/2022 07:08:11
Right so answer to Part B is 3 because both lines are parallel, thus will never meet, and thus have no solutions
1
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help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 07:08:20
yeah
0
1
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help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 07:08:29
but c1 is not equal to c2 here
0
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help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 07:08:33
when m=3
0
1
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help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 07:08:35
Yes it is
1
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5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 07:08:50
This =1
1
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help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 07:08:51
3x+my-5=0 and (m+2)x+5y-m=0
0
1
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help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 07:08:53
Not =-1
1
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help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 07:08:55
when m=3
0
1
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help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 07:09:14
3x+3y-5=0 and 5x+5y-3=0
0
1
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help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 07:09:22
These are the slopes dude..
1
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TeXit
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5c401f58b5854f3c8036a2204e3dcecf
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Deleted User
01/28/2022 07:09:29
-3/m is slope 1
1
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help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 07:09:39
(-m-2)/5 is slope 2
1
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help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 07:09:40
m=3
1
0
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help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 07:09:46
They both =-1 when m=3
1
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help-1
5c401f58b5854f3c8036a2204e3dcecf
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Deleted User
01/28/2022 07:09:59
Slope 1 = Slope 2 Thus parallel Thus no solutions
1
0
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help-1
5c401f58b5854f3c8036a2204e3dcecf
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HeadShotCem
01/28/2022 07:10:08
c1 and c2 doesn’t represent the slopes lol
0
1
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help-1
5c401f58b5854f3c8036a2204e3dcecf
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HeadShotCem
01/28/2022 07:10:18
true
0
1
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help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 07:10:19
My bad
1
0
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help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 07:10:27
I just copied you cause you said c1 != c2
1
0
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help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 07:10:39
I thought c1 and c2 were the slopes because we were just discussing the slopes
1
0
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help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 07:10:43
Anyways thats it I think
1
0
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help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 07:10:46
Thanks for the help
1
0
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help-1
5c401f58b5854f3c8036a2204e3dcecf
277,133,612,812,468,220
HeadShotCem
01/28/2022 07:10:51
you’re welcome
0
1
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help-1
5c401f58b5854f3c8036a2204e3dcecf
456,226,577,798,135,800
Deleted User
01/28/2022 07:10:54
.close
1
0
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:29:45
Hello
1
0
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:29:54
I'm not sure how this argument works
1
0
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:29:56
https://cdn.discordapp.c…4526/unknown.png
unknown.png
1
0
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:29:59
In particular
1
0
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:30:11
Wait
1
0
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:30:19
https://cdn.discordapp.c…4764/unknown.png
unknown.png
1
0
null
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null
null
205,701
help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:30:23
This is the corollary mentioned
1
0
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:30:32
About Taylor Polynomials
1
0
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:30:36
In particular
1
0
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:31:10
I can't see why according to corollary, the "new" expression of arctan x must be a Taylor Polynomial, provided that the limit is 0
1
0
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:31:32
https://cdn.discordapp.c…4544/unknown.png
unknown.png
1
0
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:31:54
It might have something to do with this theorem, however, I'm not sure how to connect the dots in rigorous manner
1
0
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:42:46
Do we hypothesize that the taylor polynomial is:
https://cdn.discordapp.c…4591/unknown.png
unknown.png
1
0
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:43:10
And just hope the limit on the specified highlight in my first screenshot is true?
1
0
638,437,422,807,384,000
du
7929
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:43:16
(which is true)
1
0
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
706,934,233,012,371,600
Ansh_
01/28/2022 07:43:37
No
0
1
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
706,934,233,012,371,600
Ansh_
01/28/2022 07:43:46
We don't "hypothesize"
0
1
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
706,934,233,012,371,600
Ansh_
01/28/2022 07:44:45
We figure this particular polynomial, **is the Taylor polynomial**, for arctan x according to the general defn of Taylor polynomials
0
1
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:45:40
This one?
https://cdn.discordapp.c…0886/unknown.png
unknown.png
1
0
null
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205,701
help-1
2e82f275d47a4a2682dc7b2c795b5e85
706,934,233,012,371,600
Ansh_
01/28/2022 07:46:08
Yes, this one is for arctan x
0
1
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205,701
help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:47:09
I can't see how this is a polynomial
1
0
null
null
null
null
null
205,701
help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:47:18
The last term is not a polynomial
1
0
null
null
null
null
null
205,701
help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:48:43
Like, reading from top to bottom, it seems like that he thinks that "if the polynomial term of arctan x expansion is actually a polynomial, then the limit must be true by Theorem 1" But I'm not sure
1
0
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
706,934,233,012,371,600
Ansh_
01/28/2022 07:51:50
No. $P$, as a polynomial, is only supposed to match $f$ up to a certain degree "n" Hence, the definition of $P_{n,a}(x)$.
0
1
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205,701
help-1
2e82f275d47a4a2682dc7b2c795b5e85
510,789,298,321,096,700
TeXit
01/28/2022 07:51:53
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
0
1
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
706,934,233,012,371,600
Ansh_
01/28/2022 07:52:14
Here.. you're just being given an example of how Taylor polynomial works
0
1
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
706,934,233,012,371,600
Ansh_
01/28/2022 07:52:29
not how it's constructed... you'll probably get that in later lessons
0
1
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
321,445,119,171,756,000
Shuri2060
01/28/2022 07:53:34
That integral is the error term
0
1
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null
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205,701
help-1
2e82f275d47a4a2682dc7b2c795b5e85
321,445,119,171,756,000
Shuri2060
01/28/2022 07:53:59
The error term isnt part of the polynomial
0
1
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null
null
205,701
help-1
2e82f275d47a4a2682dc7b2c795b5e85
755,831,671,588,126,700
RepliedPencil
01/28/2022 07:54:53
Exactly
0
1
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
755,831,671,588,126,700
RepliedPencil
01/28/2022 07:55:01
Avoid the last integral
0
1
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null
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205,701
help-1
2e82f275d47a4a2682dc7b2c795b5e85
755,831,671,588,126,700
RepliedPencil
01/28/2022 07:56:20
What a taylor polynomial means is that as you take the n derivatives of the function f(x), the degree of the polynomial (a) is always <= n
0
1
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205,701
help-1
2e82f275d47a4a2682dc7b2c795b5e85
186,109,587,366,215,680
Omegabet_
01/28/2022 07:56:48
Taylor*
0
1
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:56:52
Oh
1
0
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help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:56:56
Yeah I can see it now
1
0
null
null
null
null
null
205,701
help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:57:04
The polynomial term must be Taylor
1
0
null
null
null
null
null
205,701
help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:57:15
By corollary (or the definition you mentioned)
1
0
null
null
null
null
null
205,701
help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:57:28
Thankyou
1
0
null
null
null
null
null
205,701
help-1
2e82f275d47a4a2682dc7b2c795b5e85
810,035,477,704,998,900
nya10
01/28/2022 07:57:29
.close
1
0
null
null
null
null
null
205,702
help-1
b27cb31142ab4efb861f0893ce72ea11
810,035,477,704,998,900
nya10
01/28/2022 07:57:47
o.o
1
0
null
null
null
null
null
205,702
help-1
b27cb31142ab4efb861f0893ce72ea11
755,831,671,588,126,700
RepliedPencil
01/28/2022 07:57:52
Yes ^ My autocorrect mmmm
0
1
null
null
null
null
null
205,702
help-1
b27cb31142ab4efb861f0893ce72ea11
435,844,366,817,427,460
ishsquish
01/28/2022 07:58:55
is a function a type of relation?
0
1
null
null
null
null
null
205,702
help-1
b27cb31142ab4efb861f0893ce72ea11
435,844,366,817,427,460
ishsquish
01/28/2022 07:59:07
might be a stupid question but yes
0
1
null
null
null
null
null
205,702
help-1
b27cb31142ab4efb861f0893ce72ea11
530,116,068,644,225,000
aD
01/28/2022 08:00:38
Yes
0
1
null
null
null
null
null
205,702
help-1
b27cb31142ab4efb861f0893ce72ea11
530,116,068,644,225,000
aD
01/28/2022 08:00:49
All functions are relations
0
1
null
null
null
null
null
205,702
help-1
b27cb31142ab4efb861f0893ce72ea11
435,844,366,817,427,460
ishsquish
01/28/2022 08:00:49
so a function is a subset of a relation?
0
1
null
null
null
null
null
205,702
help-1
b27cb31142ab4efb861f0893ce72ea11
530,116,068,644,225,000
aD
01/28/2022 08:01:01
Yes
0
1
null
null
null
null
null
205,702
help-1
b27cb31142ab4efb861f0893ce72ea11
435,844,366,817,427,460
ishsquish
01/28/2022 08:01:20
okay cool
0
1
null
null
null
null
null
205,702
help-1
b27cb31142ab4efb861f0893ce72ea11
530,116,068,644,225,000
aD
01/28/2022 08:01:28
A function is a special relation
0
1
null
null
null
null
null
205,702
help-1
b27cb31142ab4efb861f0893ce72ea11
530,116,068,644,225,000
aD
01/28/2022 08:01:34
Where multiple outputs
0
1
null
null
null
null
null
205,702
help-1
b27cb31142ab4efb861f0893ce72ea11
530,116,068,644,225,000
aD
01/28/2022 08:01:45
Cannot have the same input
0
1
null
null
null
null
null
205,702
help-1
b27cb31142ab4efb861f0893ce72ea11
435,844,366,817,427,460
ishsquish
01/28/2022 08:02:00
can two outputs be the same?
0
1
null
null
null
null
null
205,702
help-1
b27cb31142ab4efb861f0893ce72ea11
530,116,068,644,225,000
aD
01/28/2022 08:02:14
Yes if the input is different
0
1
null
null
null
null
null
205,702
help-1
b27cb31142ab4efb861f0893ce72ea11
530,116,068,644,225,000
aD
01/28/2022 08:02:19
For example
0
1
504,278,422,521,118,700
kasperky
5519
kasperky
false
205,702
help-1
b27cb31142ab4efb861f0893ce72ea11
530,116,068,644,225,000
aD
01/28/2022 08:02:37
F(1) can equal 2
0
1
null
null
null
null
null
205,702
help-1
b27cb31142ab4efb861f0893ce72ea11
530,116,068,644,225,000
aD
01/28/2022 08:02:53
And f(2) cancan equal 2
0
1
null
null
null
null
null