Problem with Cantors Diagonalization Proof.

You haven't shown my logic is flawed: "It is easy to postulate an process that continues infinitely, but then turning around and supposing the process ends is unsound logic."

Saying we only need a list until the finite nth number is not the requirement of Cantor's argument. You cannot postulate a list that goes to n for all finite n because then the process doesn't end.
 
Last edited:
Do a thought experiment: make the continuing list in mind and see if you can change the number at infinity.
 
5330a78143387c32a34775495f887376.gif
 
talanum1 said:
Do a thought experiment: make the continuing list in mind and see if you can change the number at infinity.
Click to expand...
if we take (1,0), a number at infinity in P^1 using the homogenous model. Then, I can change it to (2,0), another number at infinity.
 
What is P^1 using the homogeneous model? The projective line? (1, 0) is a pair of numbers!
 
Your excursion into Projective Space does not prove you can change the infinitely indexed real number.
 
You misunderstood the proof, you can't get away with changing a finitely indexed number.
 
You must log in or register to reply here.
Back
Top
Sign up to the MyBroadband newsletter
X