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)
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)