Problems that are wrong that I must find errors

[Jkohn]

Basically what I am trying to do is solve problems by finding errors in the run down of the problem.
An example would be one of those proofs that 1=2, debunking them. I want to find problems like that; a lot harder and more relevant to what I am learning. Would like it for single variable calculus and also for classical mechanics..
Any recommendations??
-cheers

**I am not sure if I posted in the correct place

 

[rustynail]

I just want to clarify things. What you want is problems in which we have found errors, and you want us to show you the problems for you to find these errors? I don't think this would yield a lot of results for you to work on. Or do you want us to give you just ANY problem and see if you can find an error in it?

What exactly are you asking here?

 

[Jkohn]

What I want are problems that are done with errors (purposely) so that I can find those errors and correct them. I am sure there is a book out there--have not found one.

 

[HallsofIvy]

Here is the "No horse of a different color" problem that occurs in many different guises.

An inductive proof that "All horses are the same color". Consider a set containing one horse. Obviously "all" horses in that set are of the same color. Assume that, for some number, k, any set of k horses must be of the same color. Let A be a set of k+1 horses. Call one the horses "a" and let B be the set of all horses in A except "a". There are now k horses in the set so they are all of the same color. Call one of the horses
"b" and let C be the set of all horses in A except "b". Again, C contains k horses and so all are of the same color. But "a" is in set C so all horses in C must be the same color as "a" and "b" is in set B so all horses in B must be the same color as "b". Since both "a" and "b" are the same color as any other horse in A they are the same color and so all horses in A are of the same color. Therefore, by induction, all the horses in any herd, of any size, must be the same color.

Where is the error in that argument?

 

[coolul007]

If you like classical geometry here is a great book of false proofs:
The Mathematical Recreations of Lewis Carroll: Pillow Problems and a Tangled Tale (Dover Recreational Math)