Consider the set of functions f from a well-ordered set X to a totally ordered set Y. For two such functions f and g, the order is determined by the values for the smallest x such that f(x) ≠ g(x).
If Y is also well-ordered and X is finite, then the resulting order is a well-order. As already shown above, if X is infinite this is in general not the case.
If X is infinite and Y has more than one element, then the resulting set YX is not a countable set, see also cardinal exponentiation. Alternatively, consider the functions f from an inversely well-ordered X to a well-ordered Y with minimum 0, restricted to those which are non-zero at only a finite subset of X. The result is well-ordered. Correspondingly we can also consider a well-ordered X and apply lexicographical order where a higher x is a more significant position. This corresponds to exponentiation of ordinal numbers YX. If X and Y are countable then the resulting set is also countable.
Consider the set of functions f from a well-ordered set X to a totally ordered set Y. For two such functions f and g, the order is determined by the values for the smallest x such that f(x) ≠ g(x).
If Y is also well-ordered and X is finite, then the resulting order is a well-order. As already shown above, if X is infinite this is in general not the case.
If X is infinite and Y has more than one element, then the resulting set YX is not a countable set, see also cardinal exponentiation. Alternatively, consider the functions f from an inversely well-ordered X to a well-ordered Y with minimum 0, restricted to those which are non-zero at only a finite subset of X. The result is well-ordered. Correspondingly we can also consider a well-ordered X and apply lexicographical order where a higher x is a more significant position. This corresponds to exponentiation of ordinal numbers YX. If X and Y are countable then the resulting set is also countable.
Does not exist (3 words btw)
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A signature? You mean like a time signature, right? Kay, how about 3/4?
rthogastropoda is one of two major taxonomic groupings of snails and slugs, an extremely large subclass within the huge class Gastropoda. (The class Gastropoda is every kind of snail and slug, from sal****er, from freshwater and from the land. The Gastropoda in turn are a group within the phylum Mollusca, which is all of the molluscs.)
In their work, The Southern Synthesis, which has become a standard reference in the field, Ponder and Lindberg (1997) showed that the Orthogastropoda is one of two subclasses of the Gastropoda, the other subclass being a very much smaller group called the Eogastropoda, which contains only 5 families of true limpets.
This subclass, Orthogastropoda, which one perhaps could call the true snails, is defined most concisely as all those gastropods which are not members of Patellogastropoda, the true limpets.
The orthogastropoda form a clade, supported by unambiguous synapomorphies. These synapomorphies (a series of characteristics that appear in its members but not in the other forms it diverged from) are the identifying characteristics of the clade.
Some of the characteristics are:
eyes with a vitreous body on eyestalks.
paired jaws, with their position free from the buccal mass
a single kidney on the right side of pericardium
a flexoglossate radula (with a flexible radular membrane). The radula is the snail's tongue, used as a rasping tool.
unpaired osphradium (olfactory organ).
lateral ciliated zones of osphradium
a single left hypobranchial gland (on organ at gill, which releases secretions, such as the reddish dye Tyrian purple).
an unpaired ctenidium (a comblike respiratory structure in certain mollusks)
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I'm Brittany's whore. what more do you want to know?