Examples
- The most well known example of an absorbing element in algebra is multiplication, where any number multiplied by zero equals zero. Zero is thus an absorbing element.
- Floating point arithmetics as defined in IEEE-754 standard contains a special value called Not-a-Number ("NaN"). It is absorbing element for every operation, ie. x+NaN=NaN+x=NaN, x-NaN=NaN-x=NaN etc.
- The set of binary relations over a set X, together with the composition of relations forms a monoid with zero, where the zero element is the empty relation (empty set).
- The closed interval H= with x∘y=min(x,y) is also a monoid with zero, and the zero element is 0.
- More examples:
| set | operation | absorber |
|---|---|---|
| real numbers | · (multiplication) | 0 |
| nonnegative integers | greatest common divisor | 1 |
| n-by-n square matrices | · (multiplication) | matrix of all zeroes |
| extended real numbers | minimum/infimum | −∞ |
| extended real numbers | maximum/supremum | +∞ |
| sets | ∩ (intersection) | { } (empty set) |
| subsets of a set M | ∪ (union) | M |
| boolean logic | ∧ (logical and) | ⊥ (falsity) |
| boolean logic | ∨ (logical or) | ⊤ (truth) |
Read more about this topic: Absorbing Element
Famous quotes containing the word examples:
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)