I once thought I could prove that the set of all natural numbers is as large as its power set. However, I was smart enough to acknowledge my limitations (What‘s more likely: That I made a mistake in my thinking I haven‘t yet noticed, or that a theorem pretty much any professional mathematician accepts as true is actually false?), so I activly searched for errors in my thinking. Eventually, I noticed that my methods only works for finite sub sets (The set of all natural numbers is, indeed, as large as the set of all FINITE subsets), but not for infinite subsets.
Eliziers method also works for all finite subsets, but not for infinite subsets
I once thought I could prove that the set of all natural numbers is as large as its power set. However, I was smart enough to acknowledge my limitations (What‘s more likely: That I made a mistake in my thinking I haven‘t yet noticed, or that a theorem pretty much any professional mathematician accepts as true is actually false?), so I activly searched for errors in my thinking. Eventually, I noticed that my methods only works for finite sub sets (The set of all natural numbers is, indeed, as large as the set of all FINITE subsets), but not for infinite subsets.
Eliziers method also works for all finite subsets, but not for infinite subsets