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The dual notion is that of a terminal object (also called terminal element): T is terminal if for every object X in C there exists exactly one morphism X → T. Initial objects are also called coterminal or universal, and terminal objects are also called final. If an object is both initial and terminal, it is called a zero object or null object.
For example, if one takes the function () that is equal to zero everywhere except at = where () =, then the supremum of the function equals one. However, its essential supremum is zero since (under the Lebesgue measure) one can ignore what the function does at the single point where is peculiar. The essential infimum is defined in a similar way.
The essential image cannot be used to distinguish functions that are almost everywhere equal: If = holds -almost everywhere, then . =. (). These two facts characterise the essential image: It is the biggest set contained in the closures of im ( g ) {\displaystyle \operatorname {im} (g)} for all g that are a.e. equal to f:
Furthermore, a module with no proper essential extension (that is, if the module is essential in another module, then it is equal to that module) is an injective module. It is then possible to prove that every module M has a maximal essential extension E(M), called the injective hull of M. The injective hull is necessarily an injective module ...
The now final forms ן ץ ף ך predate their non-final counterparts; They were the default forms used in any position within a word. Their descender eventually bent forwards when preceding another letter to facilitate writing. [citation needed] A final form of these letters is also called pshuta (פשוטה , meaning extended or plain).
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The notion of essential uniqueness presupposes some form of "sameness", which is often formalized using an equivalence relation. A related notion is a universal property, where an object is not only essentially unique, but unique up to a unique isomorphism [1] (meaning that it has trivial automorphism group). In general there can be more than ...
Each account in the chart of accounts is typically assigned a name. Accounts may also be assigned a unique account number by which the account can be identified. Account numbers may be structured to suit the needs of an organization, such as digit/s representing a division of the company, a department, the type of account, etc.