Comparison With Nonempty Sets
In classical mathematics, a set is inhabited if and only if it is not the empty set. These definitions diverge in constructive mathematics, however. A set A is nonempty if it is not empty, that is, if
It is inhabited if
In intuitionistic logic, the negation of a universal quantifier is weaker than an existential quantifier, not equivalent to it as in classical logic.
Read more about this topic: Inhabited Set
Famous quotes containing the words comparison with, comparison and/or sets:
“I have travelled a good deal in Concord; and everywhere, in shops, and offices, and fields, the inhabitants have appeared to me to be doing penance in a thousand remarkable ways.... The twelve labors of Hercules were trifling in comparison with those which my neighbors have undertaken; for they were only twelve, and had an end; but I could never see that these men slew or captured any monster or finished any labor.”
—Henry David Thoreau (1817–1862)
“The difference between human vision and the image perceived by the faceted eye of an insect may be compared with the difference between a half-tone block made with the very finest screen and the corresponding picture as represented by the very coarse screening used in common newspaper pictorial reproduction. The same comparison holds good between the way Gogol saw things and the way average readers and average writers see things.”
—Vladimir Nabokov (1899–1977)
“Whether changes in the sibling relationship during adolescence create long-term rifts that spill over into adulthood depends upon the ability of brothers and sisters to constantly redefine their connection. Siblings either learn to accept one another as independent individuals with their own sets of values and behaviors or cling to the shadow of the brother and sister they once knew.”
—Jane Mersky Leder (20th century)