14,747
edits
Collatz conjecture: Difference between revisions
From 2nd Book
Jump to navigationJump to search
Undo revision 10962 by Pig (talk)
(Blanked the page) Tags: Blanking Reverted |
Tag: Undo |
||
| Line 1: | Line 1: | ||
https://duckduckgo.com/?q=collatz+conjecture&t=newext&atb=v369-1&iax=videos&ia=videos&iai=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D094y1Z2wpJg | |||
https://2ndbook.org/wiki/File:Collatz_formal.pdf | |||
----If someone were to prove the Collatz conjecture, here are some Socratic questions that could stimulate deep reflection and discussion: | |||
## '''What did we assume to be true in the proof?''' | |||
##* What things did we take for granted when proving it? Could there be other ideas that would lead us to different results? | |||
## '''How does the proof look at even and odd numbers?''' | |||
##* Why is it important to treat even and odd numbers differently in the Collatz sequence? How does this change the way the proof works? | |||
## '''What does the proof tell us about math problems?''' | |||
##* If the Collatz Conjecture is true, what does that tell us about other math problems that seem simple but are really hard to solve? | |||
## '''What role did computers play in proving the conjecture?''' | |||
##* How did using computers help in solving the Collatz Conjecture? Does this change the way we think about math proofs—are computers just as important as thinking with paper and pencil? | |||
## '''What new questions does the proof bring up?''' | |||
##* Now that the Collatz Conjecture is proven, what new questions or ideas can we explore? Did it help us notice other patterns in math? | |||
## '''Can this proof help solve other math problems?''' | |||
##* Are there other problems that are similar to the Collatz Conjecture? Could the ideas from this proof help us solve them too? | |||
## '''What does the proof teach us about patterns in math?''' | |||
##* Why does the Collatz sequence seem so strange and unpredictable, but still turn out to have a solution? What does this teach us about finding patterns in math? | |||
## '''What does the proof mean for the bigger picture of math?''' | |||
##* Does proving the Collatz Conjecture change how we think about math and what is possible to know? How does this affect how we search for answers in math? | |||
## '''How do we know the proof is correct?''' | |||
##* What steps do we take to make sure the proof is really right? How do we double-check to avoid mistakes in the reasoning? | |||
## '''Does this proof change how we solve math problems?''' | |||
#* Now that we have proven the Collatz Conjecture, does it change the way we should approach other unsolved math problems? Can we use the same techniques for other problems? | |||
These questions focus on probing deeper into the implications, methods, and broader context of the proof of the Collatz conjecture, encouraging reflection on both the technical and philosophical aspects of the discovery. | |||
