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help-10
53818f8448954e0b849cbf287a9ff12a
307,070,375,735,459,840
abs_0
03/26/2022 01:42:03
Okay so in short: Calculus doesn't care about right-invertibility because you can make any injective function surjective by restricting the codomain to the range at any time, and the function itself wouldn't practically change. However, if you've got a surjective function and restrict the domain so that it's injective,...
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help-10
53818f8448954e0b849cbf287a9ff12a
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.nai
03/26/2022 01:43:07
Yep
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help-10
53818f8448954e0b849cbf287a9ff12a
197,677,205,382,365,200
.nai
03/26/2022 01:43:14
That's the conclusion
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help-10
53818f8448954e0b849cbf287a9ff12a
307,070,375,735,459,840
abs_0
03/26/2022 01:43:19
Awesome
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help-10
53818f8448954e0b849cbf287a9ff12a
307,070,375,735,459,840
abs_0
03/26/2022 01:43:24
That makes sense now
1
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help-10
53818f8448954e0b849cbf287a9ff12a
197,677,205,382,365,200
.nai
03/26/2022 01:43:35
Take care now, I'm gonna debate whether I should sleep or just go 30h without
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help-10
53818f8448954e0b849cbf287a9ff12a
307,070,375,735,459,840
abs_0
03/26/2022 01:43:40
Haha ok
1
0
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help-10
53818f8448954e0b849cbf287a9ff12a
307,070,375,735,459,840
abs_0
03/26/2022 01:43:43
Thanks for the discussion
1
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help-10
53818f8448954e0b849cbf287a9ff12a
307,070,375,735,459,840
abs_0
03/26/2022 01:43:46
See ya
1
0
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help-10
53818f8448954e0b849cbf287a9ff12a
197,677,205,382,365,200
.nai
03/26/2022 01:43:51
Bye
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help-10
53818f8448954e0b849cbf287a9ff12a
307,070,375,735,459,840
abs_0
03/26/2022 01:43:52
.close
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 03:48:34
how do i prove that |a|=0 iff a = 0?
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 03:48:51
i know that it's really obvious but i don't feel good without a proof
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 03:49:47
and i know there's a property of the absolute value that says |a|=0 <=> a = 0 (Positive-definiteness) but how can i prove that?
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help-10
d5edad862b0a4aff862f0c3d72b84093
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dino dik
03/26/2022 03:53:15
you can individually prove the forward and backward implications of $\abs{a}=0\iff a=0$
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help-10
d5edad862b0a4aff862f0c3d72b84093
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TeXit
03/26/2022 03:53:17
**dino**
https://cdn.discordapp.c…240898789376.png
328019240898789376.png
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studyinglatte
03/26/2022 03:54:03
sorry but i don't really get that
1
0
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help-10
d5edad862b0a4aff862f0c3d72b84093
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dino dik
03/26/2022 03:56:33
hmm, does it make sense if I say if we prove $\abs{a}=0\implies a=0$ and prove $a=0\implies \abs{a}=0$ then that proves your iff
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d5edad862b0a4aff862f0c3d72b84093
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TeXit
03/26/2022 03:57:08
**dino**
https://cdn.discordapp.c…240898789376.png
328019240898789376.png
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 03:57:45
yeah that'll make sense, but i don't know how to prove |a|=0 => a = 0 and the other way around
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 03:58:43
would appreciate if you can prove that
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help-10
d5edad862b0a4aff862f0c3d72b84093
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dino dik
03/26/2022 03:58:44
well let's try a = 0 => |a| = 0 first
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studyinglatte
03/26/2022 03:58:58
alright
1
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d5edad862b0a4aff862f0c3d72b84093
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dino dik
03/26/2022 03:59:25
so we have a = 0, then it's clear that the absolute value of a is...?
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help-10
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studyinglatte
03/26/2022 04:01:30
by the absolute value definition if a>=0, then |a| = a. so if a = 0, then |a| = 0
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help-10
d5edad862b0a4aff862f0c3d72b84093
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dino dik
03/26/2022 04:02:14
if a>=0, then |a|=0 or |a|=a?
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 04:04:09
so if a>=b, then (what i think) a > b or a = b
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help-10
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studyinglatte
03/26/2022 04:04:22
if this is true, then what you said is also true i believe
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help-10
d5edad862b0a4aff862f0c3d72b84093
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dino dik
03/26/2022 04:05:21
yeah that's true but I'm just letting you double check your first sentence before
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help-10
d5edad862b0a4aff862f0c3d72b84093
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dino dik
03/26/2022 04:05:26
> by the absolute value definition if a>=0, then |a| = 0
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 04:06:17
oh my bad
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 04:06:20
i did a typo
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 04:06:36
i meant if a>=0, then |a| = a
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help-10
d5edad862b0a4aff862f0c3d72b84093
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dino dik
03/26/2022 04:06:56
cool cool, this is good then
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help-10
d5edad862b0a4aff862f0c3d72b84093
328,019,240,898,789,400
dino dik
03/26/2022 04:07:10
now |a|=0 => a=0
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studyinglatte
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 04:08:07
since 0>=0, then yes i believe
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 04:08:15
|0| = 0
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d5edad862b0a4aff862f0c3d72b84093
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dino dik
03/26/2022 04:09:33
that doesn't quite work, you seemed to have used the to-be-proved statement in your proof
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 04:09:54
wait did I?
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help-10
d5edad862b0a4aff862f0c3d72b84093
328,019,240,898,789,400
dino dik
03/26/2022 04:10:02
you said 0>=0
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dino dik
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help-10
d5edad862b0a4aff862f0c3d72b84093
328,019,240,898,789,400
dino dik
03/26/2022 04:10:06
but we don't know that a=0 yet
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 04:10:19
ohh right
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help-10
d5edad862b0a4aff862f0c3d72b84093
328,019,240,898,789,400
dino dik
03/26/2022 04:10:35
unless you meant the 0 in |a| = 0? but that doesn't tell us much since in |b| = 2, 2 is greater than 0 but b could be -2
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 04:11:22
ahh yeah
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 04:11:24
good point
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 04:11:51
so we still don't know if a is only 0 if given |a| = 0
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help-10
d5edad862b0a4aff862f0c3d72b84093
328,019,240,898,789,400
dino dik
03/26/2022 04:12:08
you could consider that |a|=b => a=b or a=-b (edit, we only need to consider the forward imp)
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 04:13:01
so |a| = b implies that a = b or a = -b?
1
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help-10
d5edad862b0a4aff862f0c3d72b84093
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dino dik
03/26/2022 04:13:14
yup, does that make sense?
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studyinglatte
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 04:14:18
aren't we kinda losing information? like the a>=0, then |a| = a or if a<0, then |a| = -a?
1
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 04:14:22
or is that not needed
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d5edad862b0a4aff862f0c3d72b84093
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dino dik
03/26/2022 04:15:15
the information of a>=0 or a<0 is only available if we know a, which we don't in this case, right?
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 04:15:53
i see
1
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help-10
d5edad862b0a4aff862f0c3d72b84093
896,245,007,533,629,400
studyinglatte
03/26/2022 04:15:55
yeap we don't
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help-10
d5edad862b0a4aff862f0c3d72b84093
328,019,240,898,789,400
dino dik
03/26/2022 04:16:13
so could you apply this to |a| = 0?
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 04:17:06
|a| = b if and only if a = 0 or a = -0 = 0
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 04:17:26
is that true?
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help-10
d5edad862b0a4aff862f0c3d72b84093
328,019,240,898,789,400
dino dik
03/26/2022 04:17:27
|a| = b? I think you meant |a| = 0
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 04:17:52
my bad
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 04:18:11
|a| = 0 if and only if a = 0 or a = -0 = 0
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help-10
d5edad862b0a4aff862f0c3d72b84093
328,019,240,898,789,400
dino dik
03/26/2022 04:18:15
perfect
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help-10
d5edad862b0a4aff862f0c3d72b84093
328,019,240,898,789,400
dino dik
03/26/2022 04:18:50
so `|a| = 0 if and only if a = 0 or a = -0 = 0` and `by the absolute value definition if a>=0, then |a| = a. so if a = 0, then |a| = 0`
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help-10
d5edad862b0a4aff862f0c3d72b84093
328,019,240,898,789,400
dino dik
03/26/2022 04:19:05
thus, `|a| = 0 iff a = 0`
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help-10
d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 04:19:16
ahh
1
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d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 04:19:20
thanks a lot
1
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d5edad862b0a4aff862f0c3d72b84093
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dino dik
03/26/2022 04:19:35
:catthumbsup:
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d5edad862b0a4aff862f0c3d72b84093
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studyinglatte
03/26/2022 04:19:38
.close
1
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cdf14c5bc02a4d90adcf92801512a28a
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Msvyx
03/26/2022 05:19:10
what are all the values of x for which x^5-3x^3+2x^2>3
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dino dik
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cdf14c5bc02a4d90adcf92801512a28a
704,179,090,395,103,200
Saccharine
03/26/2022 05:44:46
I assume you could find the roots and do derivative tests?
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help-10
cdf14c5bc02a4d90adcf92801512a28a
704,179,090,395,103,200
Saccharine
03/26/2022 05:44:50
maybe finding the roots is going to be hard
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help-10
cdf14c5bc02a4d90adcf92801512a28a
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Msvyx
03/26/2022 05:46:54
i still didnt take derivatives
1
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Msvyx
03/26/2022 05:47:12
i can get the answer choices if that makes it better
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studyinglatte
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Msvyx
03/26/2022 06:01:24
.close
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5a72ef1725804dde9ccdc340d0068d8a
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xenoooo
03/26/2022 06:20:27
https://cdn.discordapp.c…20326_181959.jpg
IMG_20220326_181959.jpg
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5a72ef1725804dde9ccdc340d0068d8a
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xenoooo
03/26/2022 06:20:27
https://cdn.discordapp.c…20326_181943.jpg
IMG_20220326_181943.jpg
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help-10
5a72ef1725804dde9ccdc340d0068d8a
598,628,024,094,818,300
xenoooo
03/26/2022 06:20:45
I don't know what to do next
1
0
328,019,240,898,789,400
dino dik
9674
dino
false
1,489
help-10
5a72ef1725804dde9ccdc340d0068d8a
715,020,322,541,273,100
Phearia
03/26/2022 06:21:42
I can help out
0
1
null
null
null
null
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help-10
5a72ef1725804dde9ccdc340d0068d8a
271,133,126,728,613,900
waler
03/26/2022 06:21:58
is this after or before you differentiated?
https://cdn.discordapp.c…0242/unknown.png
unknown.png
0
1
null
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null
null
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help-10
5a72ef1725804dde9ccdc340d0068d8a
598,628,024,094,818,300
xenoooo
03/26/2022 06:22:41
The x^2 + y^2 is before I diff
1
0
328,019,240,898,789,400
dino dik
9674
dino
false
1,489
help-10
5a72ef1725804dde9ccdc340d0068d8a
271,133,126,728,613,900
waler
03/26/2022 06:23:03
ok then, try again from the begining
0
1
null
null
null
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help-10
5a72ef1725804dde9ccdc340d0068d8a
271,133,126,728,613,900
waler
03/26/2022 06:23:37
remember, once you have started differentiating **both sides**, you differentiate **both sides** at once
0
1
null
null
null
null
null
1,489
help-10
5a72ef1725804dde9ccdc340d0068d8a
271,133,126,728,613,900
waler
03/26/2022 06:23:43
also remember that y is a function of x
0
1
null
null
null
null
null
1,489
help-10
5a72ef1725804dde9ccdc340d0068d8a
271,133,126,728,613,900
waler
03/26/2022 06:23:51
meaning the derivative of y wrt x is not simply 1
0
1
null
null
null
null
null
1,489
help-10
5a72ef1725804dde9ccdc340d0068d8a
598,628,024,094,818,300
xenoooo
03/26/2022 06:24:44
Okay lemme try again
1
0
null
null
null
null
null
1,489
help-10
5a72ef1725804dde9ccdc340d0068d8a
598,628,024,094,818,300
xenoooo
03/26/2022 06:28:10
https://cdn.discordapp.c…20326_182753.jpg
IMG_20220326_182753.jpg
1
0
null
null
null
null
null
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help-10
5a72ef1725804dde9ccdc340d0068d8a
598,628,024,094,818,300
xenoooo
03/26/2022 06:28:29
I got this but what should I do after that? Should I transpose?
1
0
null
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null
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help-10
5a72ef1725804dde9ccdc340d0068d8a
271,133,126,728,613,900
waler
03/26/2022 06:28:39
again, the derivative of y with respect to x is not 1
0
1
null
null
null
null
null
1,489
help-10
5a72ef1725804dde9ccdc340d0068d8a
271,133,126,728,613,900
waler
03/26/2022 06:28:48
the derivative of y wrt x is dy/dx
0
1
null
null
null
null
null
1,489
help-10
5a72ef1725804dde9ccdc340d0068d8a
271,133,126,728,613,900
waler
03/26/2022 06:33:25
if you are still having trouble, i'll do half of this for you as an example. In this problem, the derivative of x+y is not 1+1, but it's 1+**dy/dx**. Or for example, the derivative of y^2 is 2y*dy/dx
0
1
null
null
null
null
null
1,489
help-10
5a72ef1725804dde9ccdc340d0068d8a
598,628,024,094,818,300
xenoooo
03/26/2022 06:34:16
Oh okay you multiplied y' to the y variable as d(u)
1
0
null
null
null
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1,489
help-10
5a72ef1725804dde9ccdc340d0068d8a
271,133,126,728,613,900
waler
03/26/2022 06:34:29
yes, aka the chain rule
0
1
704,179,090,395,103,200
Saccharine
3780
Saccharine
false
1,489
help-10
5a72ef1725804dde9ccdc340d0068d8a
598,628,024,094,818,300
xenoooo
03/26/2022 06:34:47
Ohhh okay, now I get it. Thanks!
1
0
null
null
null
null
null
1,489
help-10
5a72ef1725804dde9ccdc340d0068d8a
598,628,024,094,818,300
xenoooo
03/26/2022 06:36:53
.close
1
0
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help-10
beb11f7fc66a412089295bd1be4d4cac
626,371,667,035,291,600
SF_19x66
03/26/2022 06:41:22
What are some examples of theorems that were derived from the idea that there are infinitely many real numbers?
1
0
null
null
null
null
null
1,490
help-10
beb11f7fc66a412089295bd1be4d4cac
279,884,747,017,289,730
Alison40
03/26/2022 06:43:36
what exactly do you mean
0
1
null
null
null
null
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1,490
help-10
beb11f7fc66a412089295bd1be4d4cac
279,884,747,017,289,730
Alison40
03/26/2022 06:44:33
do you mean there being infinite real numbers in any line segment on the real number line
0
1
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null
null
null
null
1,490
help-10
beb11f7fc66a412089295bd1be4d4cac
279,884,747,017,289,730
Alison40
03/26/2022 06:44:47
or that the real numbers go on forever
0
1
598,628,024,094,818,300
xenoooo
8707
xenoooo
false
1,490
help-10
beb11f7fc66a412089295bd1be4d4cac
626,371,667,035,291,600
SF_19x66
03/26/2022 06:46:46
this
1
0
null
null
null
null
null
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help-10
beb11f7fc66a412089295bd1be4d4cac
279,884,747,017,289,730
Alison40
03/26/2022 06:49:05
well
0
1
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null
null
null
null
1,490
help-10
beb11f7fc66a412089295bd1be4d4cac
279,884,747,017,289,730
Alison40
03/26/2022 06:49:33
limits to infinity wouldn't be as useful
0
1
null
null
null
null
null