mikeion/mathconverse_pseudonyms · Datasets at Hugging Face

conversation_id int64 1 206k	help_channel stringlengths 6 7	__rowid__ stringlengths 32 32	author_id stringlengths 17 19	author_name stringlengths 6 21	timestamp stringlengths 19 19	content stringlengths 0 3.97k	url stringlengths 0 591	fileName stringlengths 0 513	student int64 0 1	helper int64 0 1	id stringlengths 3 19	name stringlengths 3 21	nickname stringlengths 3 21	isBot stringclasses 3 values	__index_level_0__ int64 0 5.45M
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 19:58:15		https://cdn.discordapp.c…5870/unknown.png	unknown.png	0	1	nan	nan	nan	nan	5,447,750
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 19:58:27		https://cdn.discordapp.c…0564/unknown.png	unknown.png	0	1	nan	nan	nan	nan	5,447,751
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 20:00:13		https://cdn.discordapp.c…8476/unknown.png	unknown.png	0	1	nan	nan	nan	nan	5,447,752
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 20:00:18		https://cdn.discordapp.c…0734/unknown.png	unknown.png	0	1	nan	nan	nan	nan	5,447,753
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 20:00:57	u=y/2			0	1	nan	nan	nan	nan	5,447,754
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 20:01:03	x^2+(u)^2=1			0	1	nan	nan	nan	nan	5,447,755
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 20:01:06	a circle			0	1	nan	nan	nan	nan	5,447,756
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 20:01:26	must I now compute the jacobian determinant?			0	1	nan	nan	nan	nan	5,447,757
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 20:04:20	u=y/2			0	1	nan	nan	nan	nan	5,447,758
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 20:04:21	v=x			0	1	nan	nan	nan	nan	5,447,759
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 20:18:10		https://cdn.discordapp.c…1814/unknown.png	unknown.png	0	1	nan	nan	nan	nan	5,447,760
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 20:18:21	this is what I assume the flux and region is suppose to look like			0	1	nan	nan	nan	nan	5,447,761
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 20:20:03		https://cdn.discordapp.c…7690/unknown.png	unknown.png	0	1	nan	nan	nan	nan	5,447,762
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 20:20:51		https://cdn.discordapp.c…1578/unknown.png	unknown.png	0	1	nan	nan	nan	nan	5,447,763
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 20:20:53	where is what I have			0	1	348696743388381195	Reese Hernandez	Reese Hernandez	False	5,447,764
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 20:20:56	but it doesn't sound right			0	1	nan	nan	nan	nan	5,447,765
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 20:21:07	the jacobian from dxdy to dvdu			0	1	nan	nan	nan	nan	5,447,766
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 20:21:09	was -1/2			0	1	929960101157146664	Christian Adams	Christian Adams	False	5,447,767
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 20:21:34	and then I needed to convert dvdu to drdtheta			0	1	nan	nan	nan	nan	5,447,768
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 20:21:39	and im not sure if I messed up that step			0	1	nan	nan	nan	nan	5,447,769
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 20:25:04	as the answer isn't provided in the exam			0	1	nan	nan	nan	nan	5,447,770
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 20:25:06	example*			0	1	nan	nan	nan	nan	5,447,771
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 20:25:10	i cant verify my work			0	1	nan	nan	nan	nan	5,447,772
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 20:30:16	the only issue I am only issue I already see is that i have negative flux when I assume it should be positive			0	1	nan	nan	nan	nan	5,447,773
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 20:40:25	:angerysad:			0	1	nan	nan	nan	nan	5,447,774
205,787	help-1	7871f668939747c989140da91e970cdc	691679326164222084	Aria Sanchez	12/23/2021 21:06:27	Is the jacobian actually -1/2?			0	1	nan	nan	nan	nan	5,447,775
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 21:07:12	I believe so			0	1	nan	nan	nan	nan	5,447,776
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 21:07:49	either that or maybe 1/2			0	1	nan	nan	nan	nan	5,447,777
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 21:09:06	still that would only be a sign change			0	1	nan	nan	nan	nan	5,447,778
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 21:09:15	and I just don't know how to verify the answer			0	1	nan	nan	nan	nan	5,447,779
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 21:09:36	it would be like			0	1	nan	nan	nan	nan	5,447,780
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 21:09:50	dxdy=\|jacobian\|dvdu			0	1	nan	nan	nan	nan	5,447,781
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 21:10:04		https://cdn.discordapp.c…2065/unknown.png	unknown.png	0	1	nan	nan	nan	nan	5,447,782
205,787	help-1	7871f668939747c989140da91e970cdc	691679326164222084	Aria Sanchez	12/23/2021 21:14:24	Shouldn't it be the other way around?			0	1	nan	nan	nan	nan	5,447,783
205,787	help-1	7871f668939747c989140da91e970cdc	691679326164222084	Aria Sanchez	12/23/2021 21:14:37	x=u, y=2v			0	1	nan	nan	nan	nan	5,447,784
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 21:15:47	maybe :holothink:			0	1	751302185194749992	Wayne Walker	Wayne Walker	False	5,447,785
205,787	help-1	7871f668939747c989140da91e970cdc	691679326164222084	Aria Sanchez	12/23/2021 21:15:51	Giving us the \|jacobian\|=2			0	1	nan	nan	nan	nan	5,447,786
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 21:23:33		https://cdn.discordapp.c…7352/unknown.png	unknown.png	0	1	751302185194749992	Wayne Walker	Wayne Walker	False	5,447,787
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 21:23:39	idk if pi seems reasonable or not			0	1	nan	nan	nan	nan	5,447,788
205,787	help-1	7871f668939747c989140da91e970cdc	691679326164222084	Aria Sanchez	12/23/2021 21:31:55	Why is it not reasonable?			0	1	nan	nan	nan	nan	5,447,789
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 21:33:13	I mean it sounds reasonable			0	1	nan	nan	nan	nan	5,447,790
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 21:33:17	I just don't know if it is correct			0	1	nan	nan	nan	nan	5,447,791
205,787	help-1	7871f668939747c989140da91e970cdc	691679326164222084	Aria Sanchez	12/23/2021 21:34:25	I don't see any mistakes			0	1	517077202618286091	Michele Jackson	Michele Jackson	False	5,447,792
205,787	help-1	7871f668939747c989140da91e970cdc	249627068046901248	Anthony Miller	12/23/2021 21:38:59	.close			0	1	nan	nan	nan	nan	5,447,793
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	169238160952393746	Kayla Brown	01/30/2022 21:58:33	:I thanks for nothing guys			1	0	nan	nan	nan	nan	5,447,794
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	709959727098101810	Tiffany Ramirez	01/30/2022 22:01:52	So, I'm kind of stuck proving that if $b_1 + ... + b_m \leq n$, then $b_1! \cdots b_m! \leq n!$			0	1	nan	nan	nan	nan	5,447,795
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	709959727098101810	Tiffany Ramirez	01/30/2022 22:02:38	I was thinking induction, but then idek what my base case would be. There's probably something more elegant			0	1	nan	nan	nan	nan	5,447,796
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:09:20	fix m, do induction on n			0	1	nan	nan	nan	nan	5,447,797
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	709959727098101810	Tiffany Ramirez	01/30/2022 22:10:32	Okay, let me try that			0	1	nan	nan	nan	nan	5,447,798
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	709959727098101810	Tiffany Ramirez	01/30/2022 22:15:53	For n=0, the base case, if $$ b_1 + \cdots+ b_m \leq 0 $$ then that means that entire sum on the LHS is 0, right?			0	1	nan	nan	nan	nan	5,447,799
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:16:12	sure, yes			0	1	nan	nan	nan	nan	5,447,800
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:16:37	of course you should be taking $b_i\geq 0$ as an assumption anyway because otherwise what is $b_i!$			0	1	nan	nan	nan	nan	5,447,801
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	709959727098101810	Tiffany Ramirez	01/30/2022 22:17:44	Right! Okay, so then for the base case, I can assume $b_i=b_j$			0	1	nan	nan	nan	nan	5,447,802
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	709959727098101810	Tiffany Ramirez	01/30/2022 22:17:55	For any i,j			0	1	nan	nan	nan	nan	5,447,803
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:20:34	and they are all 0, zat important			0	1	nan	nan	nan	nan	5,447,804
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	709959727098101810	Tiffany Ramirez	01/30/2022 22:21:11	Okay, I think I got the base case. One sec			0	1	nan	nan	nan	nan	5,447,805
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	709959727098101810	Tiffany Ramirez	01/30/2022 22:24:05		https://cdn.discordapp.c…461450/image.png	image.png	0	1	nan	nan	nan	nan	5,447,806
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:24:35	yeh			0	1	nan	nan	nan	nan	5,447,807
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	709959727098101810	Tiffany Ramirez	01/30/2022 22:29:39	For the inductive case, the assumption is that $$ b_1 + \cdots + b_m \leq n. $$ So, I am proving that if $$ b_1! \cdots b_m! \leq n! $$, then $$ b_1! \cdots b_m! \leq (n+1)! $$ right?			0	1	nan	nan	nan	nan	5,447,808
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:31:04	no			0	1	nan	nan	nan	nan	5,447,809
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	709959727098101810	Tiffany Ramirez	01/30/2022 22:31:13	Oh what			0	1	nan	nan	nan	nan	5,447,810
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:31:36	$P(n)$ is the predicate: If $b_1 + ... + b_m \leq n$, then $b_1! \cdots b_m! \leq n!$			0	1	nan	nan	nan	nan	5,447,811
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:32:43	the base case should read: If $b_1 + \dots + b_m \leq 0$, then $b_1!\dots b_m! \leq 0!$			0	1	776947027153125416	Deanna Allen	Deanna Allen	False	5,447,812
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	709959727098101810	Tiffany Ramirez	01/30/2022 22:33:28	Oh, right. So then P(n+1) is If $b_1 + \dots + b_m \leq (n+1)$, then $b_1!\dots b_m! \leq (n+1)!$?			0	1	250608449702985731	Amy Miller	Amy Miller	False	5,447,813
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:33:42	yes			0	1	nan	nan	nan	nan	5,447,814
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	709959727098101810	Tiffany Ramirez	01/30/2022 22:34:55	Wait, so then my inductive hypothesis is only $$b_1 + \dots + b_m \leq (n+1)!$$			0	1	nan	nan	nan	nan	5,447,815
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:37:02	your inductive hypothesis is P(n)			0	1	nan	nan	nan	nan	5,447,816
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:37:15	that is: If $b_1 + ... + b_m \leq n$, then $b_1! \cdots b_m! \leq n!$			0	1	nan	nan	nan	nan	5,447,817
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:37:28	this is your inductive hypothesis			0	1	nan	nan	nan	nan	5,447,818
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:38:04	now you need to prove: if $b_1 + \dots + b_m \leq (n+1)$, then $b_1! \dots b_m! \leq (n+1)!$			0	1	776947027153125416	Deanna Allen	Deanna Allen	False	5,447,819
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	709959727098101810	Tiffany Ramirez	01/30/2022 22:39:07	Oh, so this is good so far then	https://cdn.discordapp.c…041877/image.png	image.png	0	1	nan	nan	nan	nan	5,447,820
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:39:29	i would find some issue with the first line's second half tbh			0	1	nan	nan	nan	nan	5,447,821
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:39:47	first green line i mean			0	1	nan	nan	nan	nan	5,447,822
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:40:21	and i have no idea where you learned the phrasing of the last two lines, but that is _not_ how you write induction			0	1	nan	nan	nan	nan	5,447,823
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	709959727098101810	Tiffany Ramirez	01/30/2022 22:40:30	Oh yeah, I'll delete that right hand side of the "and"			0	1	nan	nan	nan	nan	5,447,824
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:40:46	isn't that what you want to show? why are you assuming it?			0	1	nan	nan	nan	nan	5,447,825
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	709959727098101810	Tiffany Ramirez	01/30/2022 22:41:54	I thought that was our inductive hypothesis?			0	1	nan	nan	nan	nan	5,447,826
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	709959727098101810	Tiffany Ramirez	01/30/2022 22:42:24	We use P(n) to prove P(n+1)?			0	1	nan	nan	nan	nan	5,447,827
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:43:19	do you want to read those lines again			0	1	nan	nan	nan	nan	5,447,828
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:43:28	this is what we want to do			0	1	nan	nan	nan	nan	5,447,829
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:43:39	the inductive hypothesis is only P(n)			0	1	nan	nan	nan	nan	5,447,830
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:43:59	which means the only assumption is P(n) _for some n_, and we want to use this to show P(n+1) is true			0	1	nan	nan	nan	nan	5,447,831
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:44:08	we cannot just assume P(n) is true for all n			0	1	nan	nan	nan	nan	5,447,832
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	709959727098101810	Tiffany Ramirez	01/30/2022 22:45:10	So, it was just an issue with the "for all" part?			0	1	nan	nan	nan	nan	5,447,833
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:47:24	yes			0	1	nan	nan	nan	nan	5,447,834
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:47:34	for all and for some are two very different things			0	1	nan	nan	nan	nan	5,447,835
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	709959727098101810	Tiffany Ramirez	01/30/2022 22:51:12	Oh, okay. So, are we pretty much just using $n \leq (n+1)$ and $n! \leq (n+1)!$ here?			0	1	nan	nan	nan	nan	5,447,836
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	709959727098101810	Tiffany Ramirez	01/30/2022 22:51:20	In the inductive case I mean			0	1	nan	nan	nan	nan	5,447,837
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:51:40	maybe you should try the induction first			0	1	nan	nan	nan	nan	5,447,838
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 22:51:42	see what happens			0	1	nan	nan	nan	nan	5,447,839
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	709959727098101810	Tiffany Ramirez	01/30/2022 23:03:49	Mkay, so I did this and I'm not quite sure what I have at my disposal to get that what I have implies that factorial product inequality for (n+1)!			0	1	nan	nan	nan	nan	5,447,840
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	709959727098101810	Tiffany Ramirez	01/30/2022 23:03:54		https://cdn.discordapp.c…058290/image.png	image.png	0	1	nan	nan	nan	nan	5,447,841
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	709959727098101810	Tiffany Ramirez	01/30/2022 23:13:03	There's no time limit for these help channels, right? I'm just going to get some food real quick			0	1	nan	nan	nan	nan	5,447,842
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 23:20:25	Well, there's a sort of time limit that's dependent on when the bot asks you if the question is resolved			0	1	nan	nan	nan	nan	5,447,843
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 23:20:31	Otherwise no			0	1	nan	nan	nan	nan	5,447,844
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 23:21:06	About the latest picture: you don't need to say m is fixed again			0	1	nan	nan	nan	nan	5,447,845
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 23:21:16	Cause you fixed it at the start			0	1	nan	nan	nan	nan	5,447,846
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 23:22:12	You should begin by letting b_1,...,b_m be positive integers such that b_1 + ... + b_m \leq n+1			0	1	nan	nan	nan	nan	5,447,847
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 23:22:37	And then now consider the product of the factorials			0	1	nan	nan	nan	nan	5,447,848
205,788	help-1	b6502d37dc67407db5152902f63ce8c4	569167697925898261	Kendra Lee	01/30/2022 23:22:43	^ continue from there			0	1	nan	nan	nan	nan	5,447,849

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 19:58:15

https://cdn.discordapp.c…5870/unknown.png

unknown.png

0

1

nan

5,447,750

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 19:58:27

https://cdn.discordapp.c…0564/unknown.png

unknown.png

0

1

nan

5,447,751

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 20:00:13

https://cdn.discordapp.c…8476/unknown.png

unknown.png

0

1

nan

5,447,752

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 20:00:18

https://cdn.discordapp.c…0734/unknown.png

unknown.png

0

1

nan

5,447,753

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 20:00:57

u=y/2

0

1

nan

5,447,754

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 20:01:03

x^2+(u)^2=1

0

1

nan

5,447,755

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 20:01:06

a circle

0

1

nan

5,447,756

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 20:01:26

must I now compute the jacobian determinant?

0

1

nan

5,447,757

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 20:04:20

u=y/2

0

1

nan

5,447,758

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 20:04:21

v=x

0

1

nan

5,447,759

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 20:18:10

https://cdn.discordapp.c…1814/unknown.png

unknown.png

0

1

nan

5,447,760

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 20:18:21

this is what I assume the flux and region is suppose to look like

0

1

nan

5,447,761

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 20:20:03

https://cdn.discordapp.c…7690/unknown.png

unknown.png

0

1

nan

5,447,762

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 20:20:51

https://cdn.discordapp.c…1578/unknown.png

unknown.png

0

1

nan

5,447,763

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 20:20:53

where is what I have

0

1

348696743388381195

Reese Hernandez

False

5,447,764

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 20:20:56

but it doesn't sound right

0

1

nan

5,447,765

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 20:21:07

the jacobian from dxdy to dvdu

0

1

nan

5,447,766

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 20:21:09

was -1/2

0

1

929960101157146664

Christian Adams

False

5,447,767

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 20:21:34

and then I needed to convert dvdu to drdtheta

0

1

nan

5,447,768

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 20:21:39

and im not sure if I messed up that step

0

1

nan

5,447,769

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 20:25:04

as the answer isn't provided in the exam

0

1

nan

5,447,770

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 20:25:06

example*

0

1

nan

5,447,771

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 20:25:10

i cant verify my work

0

1

nan

5,447,772

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 20:30:16

the only issue I am only issue I already see is that i have negative flux when I assume it should be positive

0

1

nan

5,447,773

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 20:40:25

:angerysad:

0

1

nan

5,447,774

205,787

help-1

7871f668939747c989140da91e970cdc

691679326164222084

Aria Sanchez

12/23/2021 21:06:27

Is the jacobian actually -1/2?

0

1

nan

5,447,775

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 21:07:12

I believe so

0

1

nan

5,447,776

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 21:07:49

either that or maybe 1/2

0

1

nan

5,447,777

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 21:09:06

still that would only be a sign change

0

1

nan

5,447,778

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 21:09:15

and I just don't know how to verify the answer

0

1

nan

5,447,779

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 21:09:36

it would be like

0

1

nan

5,447,780

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 21:09:50

dxdy=|jacobian|dvdu

0

1

nan

5,447,781

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 21:10:04

https://cdn.discordapp.c…2065/unknown.png

unknown.png

0

1

nan

5,447,782

205,787

help-1

7871f668939747c989140da91e970cdc

691679326164222084

Aria Sanchez

12/23/2021 21:14:24

Shouldn't it be the other way around?

0

1

nan

5,447,783

205,787

help-1

7871f668939747c989140da91e970cdc

691679326164222084

Aria Sanchez

12/23/2021 21:14:37

x=u, y=2v

0

1

nan

5,447,784

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 21:15:47

maybe :holothink:

0

1

751302185194749992

Wayne Walker

False

5,447,785

205,787

help-1

7871f668939747c989140da91e970cdc

691679326164222084

Aria Sanchez

12/23/2021 21:15:51

Giving us the |jacobian|=2

0

1

nan

5,447,786

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 21:23:33

https://cdn.discordapp.c…7352/unknown.png

unknown.png

0

1

751302185194749992

Wayne Walker

False

5,447,787

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 21:23:39

idk if pi seems reasonable or not

0

1

nan

5,447,788

205,787

help-1

7871f668939747c989140da91e970cdc

691679326164222084

Aria Sanchez

12/23/2021 21:31:55

Why is it not reasonable?

0

1

nan

5,447,789

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 21:33:13

I mean it sounds reasonable

0

1

nan

5,447,790

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 21:33:17

I just don't know if it is correct

0

1

nan

5,447,791

205,787

help-1

7871f668939747c989140da91e970cdc

691679326164222084

Aria Sanchez

12/23/2021 21:34:25

I don't see any mistakes

0

1

517077202618286091

Michele Jackson

False

5,447,792

205,787

help-1

7871f668939747c989140da91e970cdc

249627068046901248

Anthony Miller

12/23/2021 21:38:59

.close

0

1

nan

5,447,793

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

169238160952393746

Kayla Brown

01/30/2022 21:58:33

:I thanks for nothing guys

1

0

nan

5,447,794

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

709959727098101810

Tiffany Ramirez

01/30/2022 22:01:52

So, I'm kind of stuck proving that if $b_1 + ... + b_m \leq n$, then $b_1! \cdots b_m! \leq n!$

0

1

nan

5,447,795

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

709959727098101810

Tiffany Ramirez

01/30/2022 22:02:38

I was thinking induction, but then idek what my base case would be. There's probably something more elegant

0

1

nan

5,447,796

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

569167697925898261

Kendra Lee

01/30/2022 22:09:20

fix m, do induction on n

0

1

nan

5,447,797

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

709959727098101810

Tiffany Ramirez

01/30/2022 22:10:32

Okay, let me try that

0

1

nan

5,447,798

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

709959727098101810

Tiffany Ramirez

01/30/2022 22:15:53

For n=0, the base case, if $$ b_1 + \cdots+ b_m \leq 0 $$ then that means that entire sum on the LHS is 0, right?

0

1

nan

5,447,799

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

569167697925898261

Kendra Lee

01/30/2022 22:16:12

sure, yes

0

1

nan

5,447,800

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

569167697925898261

Kendra Lee

01/30/2022 22:16:37

of course you should be taking $b_i\geq 0$ as an assumption anyway because otherwise what is $b_i!$

0

1

nan

5,447,801

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

709959727098101810

Tiffany Ramirez

01/30/2022 22:17:44

Right! Okay, so then for the base case, I can assume $b_i=b_j$

0

1

nan

5,447,802

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

709959727098101810

Tiffany Ramirez

01/30/2022 22:17:55

For any i,j

0

1

nan

5,447,803

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

569167697925898261

Kendra Lee

01/30/2022 22:20:34

and they are all 0, zat important

0

1

nan

5,447,804

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

709959727098101810

Tiffany Ramirez

01/30/2022 22:21:11

Okay, I think I got the base case. One sec

0

1

nan

5,447,805

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

709959727098101810

Tiffany Ramirez

01/30/2022 22:24:05

https://cdn.discordapp.c…461450/image.png

image.png

0

1

nan

5,447,806

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

569167697925898261

Kendra Lee

01/30/2022 22:24:35

yeh

0

1

nan

5,447,807

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

709959727098101810

Tiffany Ramirez

01/30/2022 22:29:39

For the inductive case, the assumption is that $$ b_1 + \cdots + b_m \leq n. $$ So, I am proving that if $$ b_1! \cdots b_m! \leq n! $$, then $$ b_1! \cdots b_m! \leq (n+1)! $$ right?

0

1

nan

5,447,808

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

569167697925898261

Kendra Lee

01/30/2022 22:31:04

no

0

1

nan

5,447,809

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

709959727098101810

Tiffany Ramirez

01/30/2022 22:31:13

Oh what

0

1

nan

5,447,810

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

569167697925898261

Kendra Lee

01/30/2022 22:31:36

$P(n)$ is the predicate: If $b_1 + ... + b_m \leq n$, then $b_1! \cdots b_m! \leq n!$

0

1

nan

5,447,811

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

569167697925898261

Kendra Lee

01/30/2022 22:32:43

the base case should read: If $b_1 + \dots + b_m \leq 0$, then $b_1!\dots b_m! \leq 0!$

0

1

776947027153125416

Deanna Allen

False

5,447,812

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

709959727098101810

Tiffany Ramirez

01/30/2022 22:33:28

Oh, right. So then P(n+1) is If $b_1 + \dots + b_m \leq (n+1)$, then $b_1!\dots b_m! \leq (n+1)!$?

0

1

250608449702985731

Amy Miller

False

5,447,813

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

569167697925898261

Kendra Lee

01/30/2022 22:33:42

yes

0

1

nan

5,447,814

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

709959727098101810

Tiffany Ramirez

01/30/2022 22:34:55

Wait, so then my inductive hypothesis is only $$b_1 + \dots + b_m \leq (n+1)!$$

0

1

nan

5,447,815

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

569167697925898261

Kendra Lee

01/30/2022 22:37:02

your inductive hypothesis is P(n)

0

1

nan

5,447,816

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

569167697925898261

Kendra Lee

01/30/2022 22:37:15

that is: If $b_1 + ... + b_m \leq n$, then $b_1! \cdots b_m! \leq n!$

0

1

nan

5,447,817

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

569167697925898261

Kendra Lee

01/30/2022 22:37:28

this is your inductive hypothesis

0

1

nan

5,447,818

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

569167697925898261

Kendra Lee

01/30/2022 22:38:04

now you need to prove: if $b_1 + \dots + b_m \leq (n+1)$, then $b_1! \dots b_m! \leq (n+1)!$

0

1

776947027153125416

Deanna Allen

False

5,447,819

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

709959727098101810

Tiffany Ramirez

01/30/2022 22:39:07

Oh, so this is good so far then

https://cdn.discordapp.c…041877/image.png

image.png

0

1

nan

5,447,820

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

569167697925898261

Kendra Lee

01/30/2022 22:39:29

i would find some issue with the first line's second half tbh

0

1

nan

5,447,821

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

569167697925898261

Kendra Lee

01/30/2022 22:39:47

first green line i mean

0

1

nan

5,447,822

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

569167697925898261

Kendra Lee

01/30/2022 22:40:21

and i have no idea where you learned the phrasing of the last two lines, but that is _not_ how you write induction

0

1

nan

5,447,823

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

709959727098101810

Tiffany Ramirez

01/30/2022 22:40:30

Oh yeah, I'll delete that right hand side of the "and"

0

1

nan

5,447,824

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

569167697925898261

Kendra Lee

01/30/2022 22:40:46

isn't that what you want to show? why are you assuming it?

0

1

nan

5,447,825

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

709959727098101810

Tiffany Ramirez

01/30/2022 22:41:54

I thought that was our inductive hypothesis?

0

1

nan

5,447,826

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

709959727098101810

Tiffany Ramirez

01/30/2022 22:42:24

We use P(n) to prove P(n+1)?

0

1

nan

5,447,827

205,788

help-1

b6502d37dc67407db5152902f63ce8c4

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Kendra Lee

01/30/2022 22:43:19

do you want to read those lines again

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Kendra Lee

01/30/2022 22:43:28

this is what we want to do

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Kendra Lee

01/30/2022 22:43:39

the inductive hypothesis is only P(n)

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Kendra Lee

01/30/2022 22:43:59

which means the only assumption is P(n) _for some n_, and we want to use this to show P(n+1) is true

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Kendra Lee

01/30/2022 22:44:08

we cannot just assume P(n) is true for all n

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Tiffany Ramirez

01/30/2022 22:45:10

So, it was just an issue with the "for all" part?

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Kendra Lee

01/30/2022 22:47:24

yes

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Kendra Lee

01/30/2022 22:47:34

for all and for some are two very different things

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Tiffany Ramirez

01/30/2022 22:51:12

Oh, okay. So, are we pretty much just using $n \leq (n+1)$ and $n! \leq (n+1)!$ here?

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Tiffany Ramirez

01/30/2022 22:51:20

In the inductive case I mean

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Kendra Lee

01/30/2022 22:51:40

maybe you should try the induction first

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Kendra Lee

01/30/2022 22:51:42

see what happens

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Tiffany Ramirez

01/30/2022 23:03:49

Mkay, so I did this and I'm not quite sure what I have at my disposal to get that what I have implies that factorial product inequality for (n+1)!

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Tiffany Ramirez

01/30/2022 23:03:54

https://cdn.discordapp.c…058290/image.png

image.png

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Tiffany Ramirez

01/30/2022 23:13:03

There's no time limit for these help channels, right? I'm just going to get some food real quick

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Kendra Lee

01/30/2022 23:20:25

Well, there's a sort of time limit that's dependent on when the bot asks you if the question is resolved

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Kendra Lee

01/30/2022 23:20:31

Otherwise no

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Kendra Lee

01/30/2022 23:21:06

About the latest picture: you don't need to say m is fixed again

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Kendra Lee

01/30/2022 23:21:16

Cause you fixed it at the start

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Kendra Lee

01/30/2022 23:22:12

You should begin by letting b_1,...,b_m be positive integers such that b_1 + ... + b_m \leq n+1

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Kendra Lee

01/30/2022 23:22:37

And then now consider the product of the factorials

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Kendra Lee

01/30/2022 23:22:43

^ continue from there

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