diagonalization argument造句

However, we cannot do this for the real numbers-see Cantor's diagonalization argument.
Sequential compactness of " B " in this metric can be shown by a diagonalization argument similar to the one employed in the proof of the Arzel? Ascoli theorem.
:Because the number constructed in the diagonalization argument ( as it is usually presented ) is guaranteed to be a real number, but not guaranteed to be a rational number.
But since the unit interval can be mapped to the whole real line, this would suggest that the cardinality of the reals is the same as that of the integers, which is nonsense, by the diagonalization argument.
If the total computable functions are enumerated via the Turing machines that produces them, then the above statement can be shown, if the proof system is sound, by a similar diagonalization argument to that used above, using the enumeration of provably total functions given earlier.
It's difficult to find diagonalization argument in a sentence. 用diagonalization argument造句挺难的

One such function, which is provable total but not primitive recursive, is Ackermann function : since it is recursively defined, it is indeed easy to prove its computability ( However, a similar diagonalization argument can also be built for all functions defined by recursive definition; thus, there are provable total functions that cannot be defined recursively ).