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Gödel sets are sometimes used in set theory to encode formulas, and are similar to Gödel numbers, except that one uses sets rather than numbers to do the encoding. In simple cases when one uses a hereditarily finite set to encode formulas this is essentially equivalent to the use of Gödel numbers, but somewhat easier to define because the ...
An example of an uninformatively named constant is int SIXTEEN = 16, while int NUMBER_OF_BITS = 16 is more descriptive. The problems associated with magic 'numbers' described above are not limited to numerical types and the term is also applied to other data types where declaring a named constant would be more flexible and communicative. [1]
Python sets are very much like mathematical sets, and support operations like set intersection and union. Python also features a frozenset class for immutable sets, see Collection types. Dictionaries (class dict) are mutable mappings tying keys and corresponding values. Python has special syntax to create dictionaries ({key: value})
For example, if there is no representable number lying between the representable numbers 1.45a70c22 hex and 1.45a70c24 hex, the ULP is 2×16 −8, or 2 −31. For numbers with a base-2 exponent part of 0, i.e. numbers with an absolute value higher than or equal to 1 but lower than 2, an ULP is exactly 2 −23 or about 10 −7 in single ...
All other four-digit numbers eventually reach 6174 if leading zeros are used to keep the number of digits at 4. For numbers with three identical digits and a fourth digit that is one higher or lower (such as 2111), it is essential to treat 3-digit numbers with a leading zero; for example: 2111 – 1112 = 0999; 9990 – 999 = 8991; 9981 – 1899 ...
This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here, is taken to have the value
For example, 15 is a composite number because 15 = 3 · 5, but 7 is a prime number because it cannot be decomposed in this way. If one of the factors is composite, it can in turn be written as a product of smaller factors, for example 60 = 3 · 20 = 3 · (5 · 4) .
Sociable Dudeney numbers and amicable Dudeney numbers are the powers of their respective roots. The number of iterations i {\displaystyle i} needed for F p , b i ( n ) {\displaystyle F_{p,b}^{i}(n)} to reach a fixed point is the Dudeney function's persistence of n {\displaystyle n} , and undefined if it never reaches a fixed point.