computable real number造句

• Computable real functions map computable real numbers to computable real numbers.
• Computable real functions map computable real numbers to computable real numbers.
• The proof uses a particular fact about computable real numbers.
• It is shown that " x " is not a computable real number.
• Every computable real number is arithmetical, and the arithmetical numbers form a subfield of the reals, as do the analytical numbers.
• As with the case of computable real numbers, it is not possible to effectively move between the two representations of limit computable reals.
• Moreover, the result continues to hold if the output probability is any positive number, and the probability of an oracle machine inquiry yielding 1 is any computable real number.
• The fact that such sequences exist means that the collection of all computable real numbers does not satisfy the least upper bound principle of real analysis, even when considering only computable sequences.
• Note that this property of decimal expansions means it's impossible to effectively identify computable real numbers defined in terms of a decimal expansion and those defined in the \ epsilon approximation sense.
• For the converse, we pick an \ epsilon computable real number " a " and generate increasingly precisce approximations until the " n " th digit after the decimal point is certain.
• A real number " x " is "'computable in the limit "'if there is a computable sequence r _ i of rational numbers ( or, which is equivalent, computable real numbers ) which converges to " x ".