Re:To Be or Not to Be – Mathematical Existence and the Axiom...
by afiori on Tuesday November 29, 2022 @11:18AM
(#33789460)
I made a mistake in the definition of f_0, here is the correct version:
f_0(A) = Mi if and only if |A| ∈ N
f_0(A) = Ma if and only if |A'| ∈ N
f_0(A) = Un if and only if |A| = ∞ ∧ |A'| = ∞
I mixed up the concept of infinite and cofinite in my previous comment, oops.
Actually I just realized that an even simpler example of a function satisfying the conditions would be f_1(A) = Un for all A, which is also the global minimum of the entire set.
f_0(A) = Mi if and only if |A| ∈ N
f_0(A) = Ma if and only if |A'| ∈ N
f_0(A) = Un if and only if |A| = ∞ ∧ |A'| = ∞
I mixed up the concept of infinite and cofinite in my previous comment, oops.
Actually I just realized that an even simpler example of a function satisfying the conditions would be f_1(A) = Un for all A, which is also the global minimum of the entire set.