Talk:Sophomore's dream

message: :Title added. —Nils von Barth (nbarth) (talk) 06:32, 12 February 2011 (UTC)
thread_title:  Cool! 

message: :Title added. —Nils von Barth (nbarth) (talk) 06:32, 12 February 2011 (UTC)
replies: text: Agreed... a reason for the name would be good to add. Privong 04:20, 16 March 2007 (UTC)
replies: text: I'm wondering the same thing. There's probably an interesting story behind it. Roger 18:11, 14 May 2007 (UTC)
replies: text: I came to the talkpage to see if this was being discussed actually. The etymology would add to the article. Mehmet Karatay 13:00, 20 June 2007 (UTC)
replies: text: I agree that some etymology would flesh this out a bit.  —Preceding unsigned comment added by 143.44.71.171 (talk) 01:28, 1 October 2007 (UTC)
replies: text: I added something, but I couldn't find an adequate reference so at the moment it's unsourced. skeptical scientist (talk) 05:18, 12 May 2008 (UTC)

text: —Nils von Barth (nbarth) (talk) 06:32, 12 February 2011 (UTC)
thread_title:  Why "sophomore's dream"? 

message: Wouldn't the second be simpler as follows?
\sum_{n=1}^\infty -(-1)^nn^{-n} = \sum_{n=1}^\infty -(-1)^{-n}n^{-n}  = - \sum_{n=1}^\infty (-n)^{-n}
I feel like the rightmost expression is much better. --Cheeser1 16:17, 9 July 2007 (UTC)
replies: text: True, but I think the current expression is in the standard form for an alternating series. Roger 16:25, 9 July 2007 (UTC)
replies: text: It's not though - it starts at a different index. --Cheeser1 01:39, 1 October 2007 (UTC)
thread_title:  Expression 

message: I don't think the graphs of the functions are very accurate - it appears that as x approaches zero, y tends to a value either slightly above or slightly below 1, when the the actual limit should be exactly 1. Maybe someone with good quality graphing software could confirm my thoughts and upload better images? Pscholl (talk) 12:57, 11 May 2008 (UTC)
thread_title:  Images 

message: The note added to the mention of Freshman's Dream seems hardly relevant. The term Freshman's Dream, in my experience, refers to that equation with real numbers $x$ and $y$, and the arithmetic operations taking on their standard denotations for real numbers, in which case it is, plain and simple, not generally true. I recommend removing the note, but if anyone feels it's necessary to discuss the exceptions that exist in modern abstract algebra I'd like to hear the rationale. 107.5.98.72 (talk) 21:59, 18 June 2011 (UTC)
replies: text: I think the note is useful, if only to prevent people from changing the text of the article proper to handle that technicality. If the note weren't there, I would have been tempted to change "the incorrect equation" to something like "the (in general) incorrect equation" or "the (over the reals) incorrect equation", both of which are clunkier and less informative. Perhaps a better rewording is possible, though. 24.220.188.43 (talk) 04:19, 3 September 2011 (UTC)
thread_title:  Note 

message: The current version states that the freshman's dream is "incorrect unless one is working over a field or unital commutative ring of prime characteristic n or a factor of n. The correct result is given by the binomial theorem." I think this is false for the nonprime case (e.g., the identity does not hold for $n=6$ on a field of characteristic 2 or 3). ~[user:Fph]  — Preceding unsigned comment added by 93.51.70.163 (talk) 20:04, 23 March 2015 (UTC)
thread_title:  Freshman's dream in finite fields 

message: \sum_{n=k+1}^\infty n^{k-n}=\int_{0}^{1} t^{k-t} dt
More at vixra.org/abs/1507.0051. To add this to the article is a good idea  — Preceding unsigned comment added by 83.237.214.103 (talk) 09:19, 20 July 2015 (UTC)
thread_title:  Generalization 

message: If this number is irrational, then how could we proof if this number is Algebraic or transcendental?  — Preceding unsigned comment added by 190.113.30.229 (talk) 20:08, 24 January 2017 (UTC)
thread_title:  Algebraic or transcendental number