Recalling the definitions of § 1, we write

for

, and

for

. Consider first how one would compute these quantities using an approximation to the real number

. If an approximation

is used which has

, then the error in the corresponding approximation to

is about

. Thus, for large n it will be impossible to compute

correctly. In addition, even for small n, it would be impossible to decide whether or not

for some

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