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As specified, the predicates associated with the <, ≤, =, ≥, > mathematical symbols (or equivalent notation in programming languages) return false on an unordered relation. So, for instance, NOT(x < y) is not logically equivalent to x ≥ y: on unordered, i.e. when x or y is NaN, the former returns true while the latter returns false ...
unordered(x, y) is true when "x is unordered with y", i.e., either x or y is a NaN. class(x) nextafter(x,y) returns the next representable value from x in the direction towards y
The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic originally established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE).
This does not violate trichotomy as long as a consistent total order is adopted: either −0 = +0 or −0 < +0 is valid. Common floating point types, however, have an exception to trichotomy: there is a special value "NaN" ( Not a Number ) such that x < NaN, x > NaN, and x = NaN are all false for all floating-point values x (including NaN itself).
In a non-Archimedean ordered field, we can find two positive elements x and y such that, for every natural number n, nx ≤ y.This means that the positive element y/x is greater than every natural number n (so it is an "infinite element"), and the positive element x/y is smaller than 1/n for every natural number n (so it is an "infinitesimal element").
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is true only if both A and B are false, or both A and B are true. Whether a symbol means a material biconditional or a logical equivalence , depends on the author’s style. x + 5 = y + 2 ⇔ x + 3 = y {\displaystyle x+5=y+2\Leftrightarrow x+3=y}
The 49ers were not happy with Campbell when he refused to play on Thursday night against the Los Angeles Rams. Campbell, a starter for 12 of the 49ers' first 13 games this season, was playing ...