Is there an error in this proof?

In summary, a proof is a logical and systematic way to demonstrate the validity of an argument or claim. It is important because it allows us to verify the truth of a statement or theorem and can be used to build upon existing knowledge and theories. Errors in a proof can be identified by carefully examining each step and ensuring that it follows the rules of logic and mathematics. Some common types of errors in proofs include incorrect assumptions, faulty logic, and mistakes in calculations or algebraic manipulations. These errors can completely invalidate a theorem, so it is important to thoroughly check and correct the proof if any errors are found.
  • #1
mr_coffee
1,629
1
Hello everyone, i was reviewing for the exam and I was working through this proof and I don't see how:

(2k+1)^2-(2k+1) + 3 = 4k^2+4k+1-2k-1+3 = 2(2k^2-k+1)+1

http://suprfile.com/src/1/3q9w3ud/Untitled-1[/URL] copy.jpg[/PLAIN]


But it is late so i maybe not seeing somthing.
 
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  • #2
If it is any help, there is an arithmetic error in the proof. Not that it makes any difference to the proof, but 4K-2K is +2K, not -2K.
 
  • #3
ahh okay that's what i wanted to make sure!
thanks!
 

Related to Is there an error in this proof?

1. What is a proof and why is it important?

A proof is a logical and systematic way to demonstrate the validity of an argument or claim. It is important because it allows us to verify the truth of a statement or theorem, and can be used to build upon existing knowledge and theories.

2. How do you identify errors in a proof?

Errors in a proof can be identified by carefully examining each step and ensuring that it follows the rules of logic and mathematics. Look for any inconsistencies, incorrect assumptions, or missing information that may lead to an incorrect conclusion. Additionally, it is helpful to have a second person review the proof for any mistakes.

3. What are some common types of errors in proofs?

Some common types of errors in proofs include incorrect assumptions, faulty logic, incorrect use of definitions or theorems, and mistakes in calculations or algebraic manipulations. Additionally, errors can also occur when the proof is incomplete or when crucial steps are omitted.

4. How can errors in a proof affect the validity of a theorem?

Errors in a proof can completely invalidate a theorem, as the proof serves as the foundation for the theorem's validity. If there is a mistake in the proof, it means that the argument or claim is not logically sound and therefore cannot be considered a true statement.

5. What should be done when an error is found in a proof?

If an error is found in a proof, it should be carefully analyzed and corrected. It may require going back to the beginning and reworking the proof or simply fixing a small mistake. It is important to thoroughly check the proof again after making any corrections to ensure that it is now valid and accurate.

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