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1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:23:27 | This dude should really edit his proof tho, I don’t think enough people do that. Just because it might be technically correct doesn’t mean it’s good or even readable | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:23:49 | x-sqrt(x^2+a)<0 for any a>0 | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:24:13 | Why | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:24:21 | well | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:24:54 | sqrt x^2= x
sqrt( x^2+a) > x | 0 | 1 | 197,677,205,382,365,200 | .nai | 9187 | .nai | false | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:25:30 | Even though sqrtx²=|x|, but ignore :) | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:27:01 | lol | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:27:32 | I guess that makes sense | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:27:38 | Sometimes I wonder how I passed calc 1... | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:27:41 | How do you deal with absolute value though | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:27:45 | I know right lol | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:28:01 | u dont think about it | 0 | 1 | 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 00:28:13 | Lmao they’re so annoying to deal with | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:28:20 | wait but no | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:28:23 | its still true | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:28:25 | Oh it doesn’t matter | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:28:29 | If x is positive, we’re good | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:28:59 | If x is negative, sqrt(x^2 + a) is positive which is obviously bigger than x which is negative | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:29:11 | yeah, exactly | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:29:23 | Lit | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:29:27 | :this: | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:29:36 | Dude I just feel incompetent | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:29:55 | This is a high school calc class, or maybe even algebra 2 | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:30:56 | The problem is that once you learn more advanced stuff, you forget to use the simpler things | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:31:08 | Yeah | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:31:12 | At least for me | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:31:21 | I was excited to find some cool way to prove bijectivity | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:31:35 | But the best answer was so much simpler | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:31:36 | An amazing comparison: limits before and after l'hopital | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:31:43 | Hahaha yeah | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:31:45 | Exactly | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:31:50 | btw about before | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:32:04 | Why'd you say the function has to be bijection? | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:32:11 | Wdym | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:32:18 | Oh to have an inverse? | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:32:29 | Yeah | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:32:35 | I thought generally when someone says f is invertible, they mean it’s both left-invertible and right-invertible | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:32:52 | Just like “associative” | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:33:13 | Should probably look those terms up | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:33:26 | We learnt about inverses in discrete math before calc | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:33:48 | in dm it had to be a bijection, but in calc, only an injection was enough | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:34:14 | IMG_6124.png | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:34:31 | I mean yeah | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:34:38 | I’ve only taken calc 1 and 2 | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:34:42 | Right right | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:34:47 | And we never ever dealt with invertibility | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:35:01 | Or injections or surjections or any of that | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:35:14 | But it makes sense that calc only cares about left-inverses | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:35:36 | True | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:35:52 | Wait I’m like | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:35:57 | Forgetting what a left inverse means | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:36:07 | Why is that sufficient? I don’t know why I just said that it makes sense | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:36:31 | g(f(x)) = x, right? Not necessarily f(g(x))? | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:36:58 | Hmm... | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:37:51 | Oh but | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:38:07 | You can restrict the range R to the codomain and its surjective then | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:38:18 | Right? | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:38:59 | Instead of having f: R->R, do f:R->R* where R* subset R | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:39:25 | and for every f(x) in R* you have an x in R that maps to y=f(x) | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:39:35 | => f is surjective? | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:39:49 | Yeah | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:40:08 | Ohhh | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:40:16 | I feel like this relates to partial functions | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:40:25 | Which is also a calc-only thing | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:40:37 | What are partial functions? | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:41:10 | It’s like a function, but not every element of the domain has to map to something | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:41:29 | It’s like how f(x) = 1/x is considered to be R -> R | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:41:56 | It is? | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:42:01 | huh | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:42:13 | No wait | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:42:14 | Well not literally | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:42:16 | But like | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:42:18 | > A partial function is often used when its exact domain of definition is not known or difficult to specify. This is the case in calculus, where, for example, the quotient of two functions is a partial function whose domain of definition cannot contain the zeros of the denominator. For this reason, in calculus, and mor... | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:42:49 | Aha | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:43:52 | "a partial function is generally called simply a function" | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:44:00 | Lets define a whole term that we wont even use | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:44:08 | lmao | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:44:25 | That confused me for a while | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:45:08 | So | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:45:17 | If you think of functions instead as partial functions | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:45:44 | Then for a “function” to have an inverse, it only needs left-invertibility | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:46:12 | That didn’t really make sense lol | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:46:15 | Whatever | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:46:20 | No no | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:46:35 | It does make sense | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:46:37 | I still don’t get why calc only cares about left-invertibility | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:46:43 | Oh rly | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 825,402,355,168,051,200 | theguy | 03/26/2022 00:46:55 | What's even the question ;-; | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:47:18 | Would you believe me if I told you there isn't one x) | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 825,402,355,168,051,200 | theguy | 03/26/2022 00:47:42 | Yes I would belive u | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:47:53 | I edited it to what we’re talking about rn | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:48:07 | Oh, bruh the pinned message is glitched | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 825,402,355,168,051,200 | theguy | 03/26/2022 00:48:28 | Screenshot_2022-03-26-10-17-57-291_com.discord.jpg | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:48:33 | Reopen it | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 825,402,355,168,051,200 | theguy | 03/26/2022 00:48:45 | I think the bot glitched | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:48:48 | Yeah | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 197,677,205,382,365,200 | .nai | 03/26/2022 00:48:55 | I guess surjectivity will fix the swap between domain and range? | 0 | 1 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:49:17 | Hmm | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:49:36 | What even is an inverse | 1 | 0 | null | null | null | null | null | |||||
1,486 | help-10 | 53818f8448954e0b849cbf287a9ff12a | 307,070,375,735,459,840 | abs_0 | 03/26/2022 00:49:39 | Lemme draw this | 1 | 0 | null | null | null | null | null |
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