Most mathematicians are happy to make use of those axioms in their proofs, although others do not, exploring instead so-called intuitionist logic or constructivist mathematics.

• 大部份数学家乐于在证明里使用这些公设，虽然也有些数学家不愿意，并以所谓的直觉逻辑（intuitionistlogic）或是构造数学（constructivistmathematics）取而代之。