Problems that are wrong that I must find errors

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Discussion Overview

The discussion revolves around the search for mathematical problems that contain intentional errors, particularly in the contexts of single variable calculus and classical mechanics. Participants are exploring examples of flawed proofs or reasoning, similar to the well-known "1=2" proofs, to identify and correct these errors.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses a desire to find problems with errors to practice identifying and correcting them, specifically in single variable calculus and classical mechanics.
  • Another participant seeks clarification on whether the request is for problems already known to contain errors or if any problem should be examined for potential errors.
  • A participant specifies that they are looking for problems that are purposely flawed, suggesting that there may be existing resources or books that compile such problems.
  • A specific example of a flawed inductive proof regarding the color of horses is presented, inviting others to identify the error in the argument.
  • A recommendation for a book containing false proofs in classical geometry is provided, which may serve as a resource for finding erroneous problems.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the exact nature of the request for problems with errors, leading to some confusion. There are multiple interpretations of what types of problems are being sought, indicating a lack of agreement on the discussion's focus.

Contextual Notes

There is uncertainty regarding the availability of resources specifically tailored to finding intentionally flawed problems in the requested subjects. The discussion also highlights the challenge of defining what constitutes an error in mathematical reasoning.

Who May Find This Useful

Individuals interested in mathematical proofs, error analysis, and those looking to enhance their problem-solving skills in calculus and classical mechanics may find this discussion relevant.

Jkohn
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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
 
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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?
 
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.
 
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?
 
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)
 

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