July 17, 2008
Too good to be true
(Question sent in by Udupendra. Thanks a lot amigo!)
Connect the equation (x + y)n = xn + yn to these identities:
Cracked by Goyal , p vs np , Ajay Parasuraman , Rohan , insufferablejake , Tathagata Chatterjee , gammafunction , sidsen , malcaluffin , rajeshvj , Srivats and shenoyvarun86.
Answer:
Check out udupendra’s comment below for the answer straight from the horse’s mouth :-)
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July 17th, 2008 at 9:17 pm, GMT -0700 ( 1216354637 )
The equation is called a ‘freshman’s dream’ as such an elegant equation is too good to be true, and therefore is not. The two identities are called a ’sophomore’s dream’ because of a similar too-good-to-be-true feel, but in this case considering that a year of study has gone in, it is actually true.
July 17th, 2008 at 9:22 pm, GMT -0700 ( 1216354950 )
From Google:
Sophomore’s Dream
July 17th, 2008 at 9:49 pm, GMT -0700 ( 1216356545 )
Aah.. the first identity is the “Freshman’s Dream”, which is a pretty bad approximation and which is an error “supposedly” made by freshmen.
The next set of identities is the “Sophomore’s Dream”, which was given by Leonard Euler’s protege, John Bernoulli, which is again, too-intuitive-to-be-true at first sight, but then, turns out to be actually valid!
July 17th, 2008 at 9:50 pm, GMT -0700 ( 1216356640 )
Sophomore’s Dream
July 17th, 2008 at 10:31 pm, GMT -0700 ( 1216359068 )
nice question!
the mistake (x+y)^n=x^n+y^n is commonly referred to as the “freshman’s dream”
while the definite integrals given are called the “sophomore’s dream”
July 17th, 2008 at 10:42 pm, GMT -0700 ( 1216359767 )
Dai! Lord Binomial is going to whack your freshman ass, as (a+b)^2 = (a^2)+(b^2)+ 2ab (atleast thats what my high school maths book used to claim :P)
And so the first equation (which is wrong) is known as the ‘freshman’s dream’, while the latter identities are called the ‘Sophomore’s Dream’
Good question.
July 17th, 2008 at 11:33 pm, GMT -0700 ( 1216362831 )
Sophomore’s Dream.
Regards,
Tathagata Chatterjee
July 18th, 2008 at 3:38 am, GMT -0700 ( 1216377531 )
The first equation is Freshman’s dream which is not true
the next two equations are known as the Sophomore’s dream which is actually true but has a too-good-to-be-true feel :-)
July 18th, 2008 at 8:30 am, GMT -0700 ( 1216395007 )
dreams of prospective scholars of varying degrees of youngness
July 18th, 2008 at 12:00 pm, GMT -0700 ( 1216407616 )
Sophomore’s Dream discovered by Bernoulli.
July 18th, 2008 at 12:02 pm, GMT -0700 ( 1216407722 )
The identities are referred to as Sophomore’s Dream => Something, too good to be true, but is in fact true.
The equation is referred to as Freshman’s Dream => The mistake, which was corrected by the Binomial Theorem.
July 18th, 2008 at 9:00 pm, GMT -0700 ( 1216440029 )
The first, wrong, identity is the so-called ‘Freshmans Dream’, the correct result for which is given by the binomial theorem.
The next 2 identities are the Sophomores Dream, which similarly, are so simplistic, and yet, true..
July 18th, 2008 at 9:08 pm, GMT -0700 ( 1216440530 )
Identity is known as the Freshman’s dream
Integrals are Sophomores dream
Quoting wiki both have
too-good-to-be-true feel… but only the latter is true