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1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/25/2022 23:30:13
Oh…
1
0
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null
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null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
510,789,298,321,096,700
TeXit
03/25/2022 23:30:14
**abs\_0**
https://cdn.discordapp.c…375735459842.png
307070375735459842.png
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
432,216,491,983,765,500
deneese
03/25/2022 23:30:37
what happened?
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/25/2022 23:30:46
The y disappeared
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/25/2022 23:31:03
So we can’t really solve for it any more… lol
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/25/2022 23:31:14
Gimme a sec maybe I messed up smth
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
432,216,491,983,765,500
deneese
03/25/2022 23:32:49
we're running out of time
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/25/2022 23:33:30
Yeah sry bruh
1
0
432,216,491,983,765,500
deneese
7361
deneese
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1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/25/2022 23:33:42
@.nai do you have any ideas
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/25/2022 23:33:59
I found the potential inverse functions
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/25/2022 23:34:16
But gave up trying to show that only 1 makes sense for the given domain
0
1
307,070,375,735,459,840
abs_0
8527
a.b.s._.0.
false
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/25/2022 23:34:51
Hmm
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
510,789,298,321,096,700
TeXit
03/25/2022 23:35:31
**.nai**
https://cdn.discordapp.c…205382365184.png
197677205382365184.png
0
1
432,216,491,983,765,500
deneese
7361
deneese
false
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
432,216,491,983,765,500
deneese
03/25/2022 23:36:11
howd u get that
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/25/2022 23:36:44
Solve the quadratic you get by multiplying by y in terms of y
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
432,216,491,983,765,500
deneese
03/25/2022 23:37:45
this one @.nai ?
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
432,216,491,983,765,500
deneese
03/25/2022 23:37:45
this one @.nai ?
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/25/2022 23:37:55
No
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/25/2022 23:38:02
This one
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
432,216,491,983,765,500
deneese
03/25/2022 23:38:25
multiply y in terms of y?
0
1
510,789,298,321,096,700
TeXit
0796
TeXit
true
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/25/2022 23:39:09
https://cdn.discordapp.c…ebra.android.jpg
Screenshot_20220326_043903_org.geogebra.android.jpg
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/25/2022 23:39:21
multiply by y, then solve quadratic
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
432,216,491,983,765,500
deneese
03/25/2022 23:39:57
giving you that
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
432,216,491,983,765,500
deneese
03/25/2022 23:40:00
okay
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/25/2022 23:40:08
@.nai I have an idea. I want to prove that for any c, there is exactly one positive x such that c = x - 1/x. Playing around with this equation: cx = x^2 - 1 x^2 - cx - 1 = 0 If this quadratic has exactly one positive root, we’re done. Right?
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/25/2022 23:41:50
$$\frac{c \pm \sqrt{c^2 + 4}}{2}$$ are the roots
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
510,789,298,321,096,700
TeXit
03/25/2022 23:41:52
**abs\_0**
https://cdn.discordapp.c…375735459842.png
307070375735459842.png
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/25/2022 23:42:29
I think so...
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/25/2022 23:43:03
The logic is “this equation has exactly one positive solution, thus the original equation has exactly one positive solution, thus it is bijective”
1
0
197,677,205,382,365,200
.nai
9187
.nai
false
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/25/2022 23:45:18
Yeah seems right
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/25/2022 23:46:32
But if you're going in this direction, it'd be easier to just derive injectivity from the definition of an inverse
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/25/2022 23:47:49
But aren’t we proving a left and right inverse? So it must be surjective as well as injective?
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
432,216,491,983,765,500
deneese
03/25/2022 23:48:36
guys im willing to put down any answer at this point
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/25/2022 23:49:03
Just write it out until this
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/25/2022 23:49:30
I can't think of a way that doesn't involve injectivity
0
1
432,216,491,983,765,500
deneese
7361
deneese
false
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
432,216,491,983,765,500
deneese
03/25/2022 23:50:00
how does that prove there is an inverse?
0
1
197,677,205,382,365,200
.nai
9187
.nai
false
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/25/2022 23:50:11
It doesn't
0
1
510,789,298,321,096,700
TeXit
0796
TeXit
true
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/25/2022 23:50:19
But at least you'll get some credit
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
432,216,491,983,765,500
deneese
03/25/2022 23:51:01
somebody had posted on the message board this initially
https://cdn.discordapp.c…6432/unknown.png
unknown.png
0
1
432,216,491,983,765,500
deneese
7361
deneese
false
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/25/2022 23:51:01
I've never really seen calc care about surjectivity for inverses, but then again I haven't done much on this topic
0
1
197,677,205,382,365,200
.nai
9187
.nai
false
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
432,216,491,983,765,500
deneese
03/25/2022 23:51:33
some of their points got redacted, but do u think this works?
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/25/2022 23:52:18
Hmm
1
0
432,216,491,983,765,500
deneese
7361
deneese
false
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/25/2022 23:53:35
I don’t really get what they’re saying
1
0
510,789,298,321,096,700
TeXit
0796
TeXit
true
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/25/2022 23:53:53
I think they’re saying if g(a) = g(b) then a = b
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/25/2022 23:54:40
a - 1/a = b - 1/b
1
0
197,677,205,382,365,200
.nai
9187
.nai
false
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
432,216,491,983,765,500
deneese
03/25/2022 23:55:35
im so tired
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
432,216,491,983,765,500
deneese
03/25/2022 23:55:37
and lost
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/25/2022 23:55:38
Hmm
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/25/2022 23:55:48
I don’t really know how they got to the first equation
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/25/2022 23:55:52
And what this contradiction mess is
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/25/2022 23:56:28
@deneese I would write this, and then the next equation
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/25/2022 23:57:17
And if you really have no time then just claim “obviously there is no way for both of these numbers to be positive. Thus this quadratic has exactly one positive root, and so our original equation has exactly one positive solution.”
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/26/2022 00:05:43
a²b-b=b²a-a a²b-b^2a-b+a=0 ba²-(b²-1)a-b=0 a=(b²-1±sqrt(b⁴-2b²+1+4b²)/2b a=(b²-1±sqrt(b⁴+2b²+1)/2b a=(b²-1±(b²+1)/2b 1) a=-1/b 2) a=b²
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/26/2022 00:05:48
Phone sucks
0
1
510,789,298,321,096,700
TeXit
0796
TeXit
true
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/26/2022 00:06:11
@abs_0 this look ok to you?
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/26/2022 00:07:02
Yep
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/26/2022 00:07:10
That’s how they got that first equation
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/26/2022 00:07:10
Wow
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/26/2022 00:08:04
But what did they do with that? Seems like they derived some sort of contradiction here
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/26/2022 00:08:14
Well yeah
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/26/2022 00:08:23
So... lemme reread it again
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/26/2022 00:08:55
Dude take a step back and realize they’re expecting high schoolers to do this problem
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/26/2022 00:08:57
Lmao
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/26/2022 00:09:03
So from the domain of the function* we know that both a and b are positive
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/26/2022 00:09:34
which is a contradiction with 1) because 1) shows them to be negative, let alone equal
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/26/2022 00:10:02
But doesn’t that imply the second case?
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/26/2022 00:10:38
How so?
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/26/2022 00:11:17
I thought 1) and 2) were cases of the last equation. Ie 1) is true *or* 2) is true
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
432,216,491,983,765,500
deneese
03/26/2022 00:12:29
it alright guys
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
432,216,491,983,765,500
deneese
03/26/2022 00:12:31
i figured it out
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/26/2022 00:12:38
Bruh what
1
0
432,216,491,983,765,500
deneese
7361
deneese
false
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/26/2022 00:12:43
Seriously?
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
307,070,375,735,459,840
abs_0
03/26/2022 00:12:49
What did you do @deneese
1
0
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/26/2022 00:13:30
Fuck 5am brain
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
432,216,491,983,765,500
deneese
03/26/2022 00:13:44
https://cdn.discordapp.c…5662/unknown.png
unknown.png
0
1
307,070,375,735,459,840
abs_0
8527
a.b.s._.0.
false
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
197,677,205,382,365,200
.nai
03/26/2022 00:15:06
Ok no, my bad. I don't see the contradiction
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
432,216,491,983,765,500
deneese
03/26/2022 00:15:38
thanks for all ur guys help
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
432,216,491,983,765,500
deneese
03/26/2022 00:15:41
even if its not right
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
432,216,491,983,765,500
deneese
03/26/2022 00:15:44
im okay with it
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
432,216,491,983,765,500
deneese
03/26/2022 00:15:53
have a great rest of ur day/night
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
432,216,491,983,765,500
deneese
03/26/2022 00:15:56
tyvm again
0
1
null
null
null
null
null
1,485
help-10
381a091c56c3457394a6bdc7c4c4ac2e
432,216,491,983,765,500
deneese
03/26/2022 00:15:58
.close
0
1
null
null
null
null
null
1,486
help-10
53818f8448954e0b849cbf287a9ff12a
307,070,375,735,459,840
abs_0
03/26/2022 00:16:01
Nice dude
1
0
null
null
null
null
null
1,486
help-10
53818f8448954e0b849cbf287a9ff12a
307,070,375,735,459,840
abs_0
03/26/2022 00:16:13
Solid proof
1
0
null
null
null
null
null
1,486
help-10
53818f8448954e0b849cbf287a9ff12a
307,070,375,735,459,840
abs_0
03/26/2022 00:16:27
Bro @.nai it was right in front of us lmao
1
0
null
null
null
null
null
1,486
help-10
53818f8448954e0b849cbf287a9ff12a
197,677,205,382,365,200
.nai
03/26/2022 00:16:42
No comment x)
0
1
null
null
null
null
null
1,486
help-10
53818f8448954e0b849cbf287a9ff12a
197,677,205,382,365,200
.nai
03/26/2022 00:16:53
At least we know more now for other problems
0
1
null
null
null
null
null
1,486
help-10
53818f8448954e0b849cbf287a9ff12a
307,070,375,735,459,840
abs_0
03/26/2022 00:16:56
Why does calculus only care about left-invertibility (i.e. injection) when considering inverses of functions
1
0
197,677,205,382,365,200
.nai
9187
.nai
false
1,486
help-10
53818f8448954e0b849cbf287a9ff12a
307,070,375,735,459,840
abs_0
03/26/2022 00:16:57
Yeah
1
0
null
null
null
null
null
1,486
help-10
53818f8448954e0b849cbf287a9ff12a
307,070,375,735,459,840
abs_0
03/26/2022 00:17:57
Why does calculus only care about left-invertibility (i.e. injection) when considering inverses of functions
1
0
null
null
null
null
null
1,486
help-10
53818f8448954e0b849cbf287a9ff12a
197,677,205,382,365,200
.nai
03/26/2022 00:19:27
right limit :pandaHmm:
0
1
null
null
null
null
null
1,486
help-10
53818f8448954e0b849cbf287a9ff12a
307,070,375,735,459,840
abs_0
03/26/2022 00:19:55
Wait @.nai isn’t this problematic? He __assumed__ there was an inverse and then showed that it didn’t lead to any contradictions
1
0
null
null
null
null
null
1,486
help-10
53818f8448954e0b849cbf287a9ff12a
307,070,375,735,459,840
abs_0
03/26/2022 00:20:04
Isn’t that a circular argument?
1
0
432,216,491,983,765,500
deneese
7361
deneese
false
1,486
help-10
53818f8448954e0b849cbf287a9ff12a
197,677,205,382,365,200
.nai
03/26/2022 00:20:50
I don't like the beginning of the proof
0
1
null
null
null
null
null
1,486
help-10
53818f8448954e0b849cbf287a9ff12a
197,677,205,382,365,200
.nai
03/26/2022 00:20:59
It has no clear list of arguments
0
1
null
null
null
null
null
1,486
help-10
53818f8448954e0b849cbf287a9ff12a
307,070,375,735,459,840
abs_0
03/26/2022 00:21:21
I suppose one could argue that the function he got at the end was a valid inverse, so technically the proof “starts” with that
1
0
null
null
null
null
null
1,486
help-10
53818f8448954e0b849cbf287a9ff12a
307,070,375,735,459,840
abs_0
03/26/2022 00:21:32
But yeah there’s no roadmap or anything
1
0
null
null
null
null
null
1,486
help-10
53818f8448954e0b849cbf287a9ff12a
197,677,205,382,365,200
.nai
03/26/2022 00:22:55
Either way this was kinda fun ngl x)
0
1
null
null
null
null
null
1,486
help-10
53818f8448954e0b849cbf287a9ff12a
307,070,375,735,459,840
abs_0
03/26/2022 00:23:10
Yeah lol
1
0
null
null
null
null
null
1,486
help-10
53818f8448954e0b849cbf287a9ff12a
197,677,205,382,365,200
.nai
03/26/2022 00:23:25
also, just now I realised
0
1
null
null
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