

Nir Dahan Inner circle Munich, Germany 1390 Posts 
Since there were a few of those posted lately I thought why not post another  sorry if it was already posted...
1 = 1 1/1 = 1/1 sqrt(1/1) = sqrt(1/1) sqrt(1)/sqrt(1) = sqrt(1)/sqrt(1) multiply in diagonals... sqrt(1) * sqrt (1) = sqrt(1) * sqrt(1) cancel the sqrt... 1 = 1 !!!!!! has the world of numbers gone bizzare ????!!! or could you help "captain math" find the error ??? 
stanalger Special user St. Louis, MO 996 Posts 
Error occurs when going from
line 3 to line 4. sqrt(a/b) = (sqrt(a)) / (sqrt(b)) only if all of the square roots are real numbers. 
James F Inner circle Atlanta 1097 Posts 
http://www.themagiccafe.com/forums/viewt......01&2
that's close to what I posted. At least the errors in the math is the same. That mistake is pretty tough to catch if you aren't up on your math. James 
Nir Dahan Inner circle Munich, Germany 1390 Posts 
Stan,
we don't assume real numbers only. complex numbers are allowed and the mistake is not there... it is somewhere else. there is a more beautiful version of this "falacy" in the Moscow puzzles book. look for the mosquito and elephant puzzle. the one in the book is even more hard to catch. Nir 
TomasB Inner circle Sweden 1143 Posts 
I guess it is from going to line 3 as you have missed writing all solutions when you take the root out of both sides of the equation. The solution you decided to keep is not the correct one.
/Tomas 
Nir Dahan Inner circle Munich, Germany 1390 Posts 
Right Tomas!
if you have the moscow puzzles book try to look up the similar problem there. that is by far more hidden in their problem... 
Jonathan Townsend Eternal Order Ossining, NY 27017 Posts 
I got lost when you suggested that i/1 == 1/i ie I = (i)**1
...to all the coins I've dropped here

stanalger Special user St. Louis, MO 996 Posts 
Jonathan,
Agreed. There is no error on line 3. The error certainly occurs when you go to line 4. Earlier I wrote: sqrt(a/b) = (sqrt(a)) / (sqrt(b)) only if all of the square roots are real numbers. I shouldn't have included the word "only". Perhaps I should have said: sqrt(a/b) = (sqrt(a))/(sqrt(b)) whenever a is a nonnegative real number and b is a positive real number. Although it is also true in some other cases, it is not true for all real a, b. Case in point: sqrt(1/1) is not equal to sqrt(1) / sqrt(1). (But sqrt(1/1) is equal to sqrt(1) / sqrt(1).) Stan 
Jonathan Townsend Eternal Order Ossining, NY 27017 Posts 
There are usually two square roots of a number. We call one of them the principal root.
...to all the coins I've dropped here

James F Inner circle Atlanta 1097 Posts 
A lot of people say the fallacy comes by not writting the "plus or minus" sign. (as stated by Nir Dahan) However, with this example the fallacy is simplifying sqrt(1/1) = sqrt(1/1) as sqrt1/sqrt1 = sqrt1/sqrt1 ...You cannot do that. Although in a lot of cases this will work it will not work all the time and it is the source of fallacy so strangler was correct. Read his explanation, it is right on.
James 
The Magic Cafe Forum Index » » Puzzle me this... » » 1 = 1 (0 Likes) 
[ Top of Page ] 
All content & postings Copyright © 20012020 Steve Brooks. All Rights Reserved. This page was created in 0.15 seconds requiring 5 database queries. 
The views and comments expressed on The Magic Café are not necessarily those of The Magic Café, Steve Brooks, or Steve Brooks Magic. > Privacy Statement < 