Proof using Axiom of Choice is Nonconstructive
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Theorem
A proof which depends upon the Axiom of Choice is a nonconstructive proof.
Proof
The Axiom of Choice allows that an infinite number of selections be made without the need to specify the choice function.
Hence such a proof is nonconstructive.
$\blacksquare$
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): nonconstructive proof