I've recently found an approach to show that the sequence generated in the famous Collatz conjecture is eventually periodic. Here is a link to the proof: https://latex.artofproblemsolving.com/miscpdf/qryxlybb.pdf?t=1720753818139
Question: Where is mistake in this proof?
I've shown that the sequence generated in the famous Collatz conjecture is eventually periodic. My proof is quite simple that looks to be impossible. But it's driving me crazy that I've already checked for several days myself and can't find any error in it.
Is it cyclic or something? Did I make l...
Simplify the expressions:
$\sqrt{121y^2}$, if $y<0$
$\sqrt{25/49c^{10}}$, if $c<0$
Math teacher whose lessons I watch on YouTube proposed such solutions:
√121y² = √121×√y² = 11×|y| = 11×(–y) = –11y
√25/49c¹⁰ = √25/√49×√c¹⁰ = 5/7×|c⁵| = 5/7×(–c⁵) = –5/7c⁵
I just can't comprehend how can we get...
@Peter I disagree with this. There's nothing wrong with that answer; a now-deleted comment criticizes it for taking ultrafinitism seriously, but (and I'm far from an ultrafinitist FWIW) that doesn't make it a bad answer. I think using CURED in this way comes dangerously close to an abuse of its purpose: we shouldn't ask for downvotes on answers just for countenancing philosophical positions we disagree with.
Simplify the expressions:
$\sqrt{121y^2}$, if $y<0$
$\sqrt{25/49c^{10}}$, if $c<0$
Math teacher whose lessons I watch on YouTube proposed such solutions:
√121y² = √121×√y² = 11×|y| = 11×(–y) = –11y
√25/49c¹⁰ = √25/√49×√c¹⁰ = 5/7×|c⁵| = 5/7×(–c⁵) = –5/7c⁵
I just can't comprehend how can we get...
