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Mathematics: √ 2 ≈ 1.414 213 562 373 095 049, the ratio of the diagonal of a square to its side length. Mathematics: φ ≈ 1.618 033 988 749 894 848, the golden ratio. Mathematics: √ 3 ≈ 1.732 050 807 568 877 293, the ratio of the diagonal of a unit cube. Mathematics: the number system understood by most computers, the binary system ...
In mathematics and computer science, the sorting numbers are a sequence of numbers introduced in 1950 by Hugo Steinhaus for the analysis of comparison sort algorithms. These numbers give the worst-case number of comparisons used by both binary insertion sort and merge sort. However, there are other algorithms that use fewer comparisons.
This is due to older software using 32-bit integers for file indexing, which limits file sizes to 2^31 bytes (2 GB) (for signed integers), or 2^32 (4 GB) (for unsigned integers). Older C programming libraries have this 2 or 4 GB limit, but the newer file libraries have been converted to 64-bit integers thus supporting file sizes up to 2^63 or 2 ...
Firstly, the order type of the set of natural numbers is ω. Any other model of Peano arithmetic, that is any non-standard model, starts with a segment isomorphic to ω but then adds extra numbers. For example, any countable such model has order type ω + (ω* + ω) ⋅ η. Secondly, consider the set V of even ordinals less than ω ⋅ 2 + 7:
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