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1,798 | help-10 | 106fcab46dc5465cb1c9c374ad27e572 | 828,122,705,659,560,000 | SDR | 04/10/2022 01:34:59 | what is arthmaetic | 1 | 0 | null | null | null | null | null | |||||
1,798 | help-10 | 106fcab46dc5465cb1c9c374ad27e572 | 711,790,477,271,105,700 | Poppiter Hellriver | 04/10/2022 01:36:50 | Emm | 0 | 1 | null | null | null | null | null | |||||
1,798 | help-10 | 106fcab46dc5465cb1c9c374ad27e572 | 711,790,477,271,105,700 | Poppiter Hellriver | 04/10/2022 01:36:54 | Basically | 0 | 1 | null | null | null | null | null | |||||
1,798 | help-10 | 106fcab46dc5465cb1c9c374ad27e572 | 711,790,477,271,105,700 | Poppiter Hellriver | 04/10/2022 01:36:57 | Calculation | 0 | 1 | null | null | null | null | null | |||||
1,798 | help-10 | 106fcab46dc5465cb1c9c374ad27e572 | 828,122,705,659,560,000 | SDR | 04/10/2022 01:37:13 | ok | 1 | 0 | null | null | null | null | null | |||||
1,798 | help-10 | 106fcab46dc5465cb1c9c374ad27e572 | 929,612,596,817,068,000 | _Anonymous | 04/10/2022 01:51:21 | ... | 0 | 1 | null | null | null | null | null | |||||
1,798 | help-10 | 106fcab46dc5465cb1c9c374ad27e572 | 485,903,210,272,391,200 | dldh06 | 04/10/2022 01:53:34 | You should probably learn the other material that leads up to quadratics | 0 | 1 | 711,790,477,271,105,700 | Poppiter Hellriver | 4400 | Poppiter Hellriver | false | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 02:16:47 | unknown.png | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 02:16:51 | idk how to do dis | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 02:22:08 | IMG_0444.png | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 02:37:30 | @heloers | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 02:37:33 | @Helpers | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:04:23 | Consider the function f(x)-x | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:04:48 | Why? | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:05:56 | We can show via intermediate value theorem that this function definitely achieves value of 0 for some x in [0,1] | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:07:02 | I don't really understand or see how | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:07:10 | Is this correct?/ | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:07:14 | like the definition of invt | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:08:47 | How did you conclude f(0)≠f(1) ? | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:11:25 | Suppose there is no c in [0,1] such that f(c)=c. That means f(0)-0>0 and f(1)-1<0. Precisely our function f(x)-x evaluated at 0 and 1 | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:12:29 | isnt that the definitiion | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:12:49 | Why does that mean that? | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:12:55 | I dont really understand | 1 | 0 | 200,013,547,491,688,450 | a disappointing son | 0540 | a disappointing son | false | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:13:38 | asdf1.PNG | 1 | 0 | 828,122,705,659,560,000 | SDR | 4086 | SDR | false | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:13:42 | Not necessarily. Consider the function f(x)=0 for all x in [0,1] it satisfies all the conditions in the question | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:14:27 | huh | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:14:41 | that doesnt make sense then does it | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:14:52 | if f(x) = 0 | 1 | 0 | 828,122,705,659,560,000 | SDR | 4086 | SDR | false | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:15:06 | Nowhere in the question does it say f(0)≠f(1) | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:15:09 | then f(a) and f(b) bound nothing | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:15:35 | Is it not implied by the actual definition of IVT that im using? | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:15:52 | But it is a valid continuous function from [0,1] to [0,1] | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:16:10 | That doesnt mean that f(c) = k | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:16:19 | i don't think we're on the same page im quite confused now | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:17:09 | IVT does require f(a)≠f(b) sure. But not necessarily the question | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:17:21 | unknown.png | 1 | 0 | 691,679,326,164,222,100 | Euclid31415 | 9927 | Euclid31415 | false | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:17:26 | reposting q for referencing | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:17:45 | from the intermediate value theorem | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:18:13 | we have to show that f(a) < k < f(b) or f(b) < k < f(a) right | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:18:24 | We are applying IVT on the function f(x)-x as i said earlier | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:18:31 | Why? | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:19:08 | Ok then tell me how does that show f(c)=c for some c in [0,1] | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:19:42 | thats my point idk lol | 1 | 0 | 691,679,326,164,222,100 | Euclid31415 | 9927 | Euclid31415 | false | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:20:13 | it's not some specific constant value analogous to "k" in the IVT | 0 | 1 | 691,679,326,164,222,100 | Euclid31415 | 9927 | Euclid31415 | false | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:21:28 | But if we do show there is some "c" in [0,1] such that f(x)-x achieves 0 there it is equivalent to saying f(c)=c | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:23:13 | hmm maybe im starting to get it | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:23:22 | so youre proiving that f(c) - c = 0 essentially | 1 | 0 | 246,174,820,088,152,060 | 99muppets | 2149 | 99muppets | false | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:23:31 | which is equivilant to f(c) = c? | 1 | 0 | 691,679,326,164,222,100 | Euclid31415 | 9927 | Euclid31415 | false | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:23:49 | In our question, we need to show f(c)=c for some c in [0,1]. IVT directly on the function f doesn't work | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:23:57 | ywyw | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:24:06 | yeye** | 1 | 0 | 246,174,820,088,152,060 | 99muppets | 2149 | 99muppets | false | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:24:10 | Yep | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:24:55 | hmm okay i am kinda understanding the goal ate last now | 1 | 0 | 691,679,326,164,222,100 | Euclid31415 | 9927 | Euclid31415 | false | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:27:00 | And now, we start with this | 0 | 1 | 246,174,820,088,152,060 | 99muppets | 2149 | 99muppets | false | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:27:34 | proof by contradiction? | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:27:59 | Well, you could also do direct proof | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:28:06 | maybe id like to try direct proof | 1 | 0 | 246,174,820,088,152,060 | 99muppets | 2149 | 99muppets | false | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:28:15 | im not completely sure where the inequalities are from im sorry | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:29:52 | They are easy to see actually. Codomain of our function f is [0,1]. Which means f(0)≥0 implying f(0)-0≥0 but if f(0)=0 we already have a contradiction. Thus we assume f(0)-0>0. And similarly for f(1)-1<0 | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:30:46 | Why does f(0) >= 0 true? | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:31:00 | oh wait | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:31:02 | sorry | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:31:19 | 1≥f(x)≥0 for all x in [0,1] | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:31:23 | ye i get that | 1 | 0 | 246,174,820,088,152,060 | 99muppets | 2149 | 99muppets | false | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:31:25 | hmm | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:31:41 | I don;t really understand | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:31:44 | Try this | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:31:52 | is this the direct proof> | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:31:53 | ? | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:32:18 | No. It was my attempt to explain the proof by contradiction earlier. Direct proof is also similar to this actually. | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:34:17 | Ignore all that lets start the proof from scratch | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:34:32 | Thank you for your patience btw 🙂 | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:34:54 | First of all, f(0)≥0 | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:36:41 | Yepp | 1 | 0 | 246,174,820,088,152,060 | 99muppets | 2149 | 99muppets | false | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:36:57 | Is it also neccesary to say that 1 >= f(0) <= 0 | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:37:20 | Well ofcourse that's where f(0)≥0 comes from | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:37:28 | okiee | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:37:47 | Well, 1>=f(0)>=0 | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:38:49 | Anyways, if we do have f(0)=0, we already have our required c | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:39:02 | Ye sure | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:39:08 | So we assume f(0)>0 which is same as saying f(0)-0>0 | 0 | 1 | 246,174,820,088,152,060 | 99muppets | 2149 | 99muppets | false | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:39:54 | sure | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:40:13 | And we do something similar for f(1)≤1 | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:40:33 | If we have f(1)=1 we have c=1 | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:40:40 | So, f(1)<1 | 0 | 1 | 246,174,820,088,152,060 | 99muppets | 2149 | 99muppets | false | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:41:05 | And ofcourse this also comes from 0≤f(1)≤1 | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:41:24 | okie dokie i get that | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:41:52 | And that's equivalent to saying f(1)-1<0 | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:42:36 | yee | 1 | 0 | 246,174,820,088,152,060 | 99muppets | 2149 | 99muppets | false | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:43:02 | Now, we consider the function f(x)-x on domain [0,1] | 0 | 1 | 691,679,326,164,222,100 | Euclid31415 | 9927 | Euclid31415 | false | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:43:59 | ye] | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:44:08 | Now we actually have f(1)-1<0<f(0)-0 combining the two inequalities from earlier | 0 | 1 | 246,174,820,088,152,060 | 99muppets | 2149 | 99muppets | false | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:45:10 | Which means we also have f(1)-1≠f(0)-0 | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:46:14 | All the required conditions for IVT are satisfied for our function f(x)-x on [0,1] | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:49:19 | f(x)-x is a continuous function on [0,1] where f(0)-0>0 and f(1)-1<0. It means there exists some c in (0,1) such that f(c)-c=0 | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:52:20 | @99muppets | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:54:30 | sorry just trying to read it over | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 246,174,820,088,152,060 | 99muppets | 04/10/2022 03:55:16 | i think i kinda get it | 1 | 0 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:55:40 | If you are uncomfortable, you can call our new function g(x). g(x)=f(x)-x | 0 | 1 | null | null | null | null | null | |||||
1,799 | help-10 | 8b8e0a45d651480d9aad0bb2f5b799b3 | 691,679,326,164,222,100 | Euclid31415 | 04/10/2022 03:56:23 | g(0)>0>g(1) | 0 | 1 | 246,174,820,088,152,060 | 99muppets | 2149 | 99muppets | false |
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