Total orderIn mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation on some set , which satisfies the following for all and in : (reflexive). If and then (transitive). If and then (antisymmetric). or (strongly connected, formerly called total). Reflexivity (1.) already follows from connectedness (4.), but is required explicitly by many authors nevertheless, to indicate the kinship to partial orders.
Lexicographic orderIn mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set. There are several variants and generalizations of the lexicographical ordering. One variant applies to sequences of different lengths by comparing the lengths of the sequences before considering their elements.
Order isomorphismIn the mathematical field of order theory, an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism for partially ordered sets (posets). Whenever two posets are order isomorphic, they can be considered to be "essentially the same" in the sense that either of the orders can be obtained from the other just by renaming of elements. Two strictly weaker notions that relate to order isomorphisms are order embeddings and Galois connections.
Self-employmentSelf-employment is the state of working for oneself rather than an employer. Tax authorities will generally view a person as self-employed if the person chooses to be recognised as such or if the person is generating income for which a tax return needs to be filed. In the real world, the critical issue for the tax authorities is not whether a person is engaged in a business activity (called "trading" even when referring to the provision of a service) but whether the activity is profitable and therefore potentially taxable.
Garden toolA garden tool is any one of many tools made for gardening and landscaping, which overlap with the range of tools made for agriculture and horticulture. Garden tools can be divided into hand tools and power tools. Hand tool Today's garden tools originated with the earliest agricultural implements used by humans. Examples include the hatchet, axe, sickle, scythe, pitchfork, spade, shovel, trowel, hoe, fork, and rake. In some places, the machete is common. The earliest tools were made variously of wood, flint, metal, tin, and bone.
At-will employmentIn United States labor law, at-will employment is an employer's ability to dismiss an employee for any reason (that is, without having to establish "just cause" for termination), and without warning, as long as the reason is not illegal (e.g. firing because of the employee's gender, sexual orientation, race, religion, or disability status). When an employee is acknowledged as being hired "at will", courts deny the employee any claim for loss resulting from the dismissal.
Hand toolA hand tool is any tool that is powered by hand rather than a motor. Categories of hand tools include wrenches, pliers, cutters, , striking tools, struck or hammered tools, screwdrivers, vises, clamps, snips, hacksaws, drills, and knives. Outdoor tools such as garden forks, pruning shears, and rakes are additional forms of hand tools. Portable power tools are not hand tools. Hand tools have been used by humans since the Stone Age when stone tools were used for hammering and cutting.
Data integrationData integration involves combining data residing in different sources and providing users with a unified view of them. This process becomes significant in a variety of situations, which include both commercial (such as when two similar companies need to merge their databases) and scientific (combining research results from different bioinformatics repositories, for example) domains. Data integration appears with increasing frequency as the volume (that is, big data) and the need to share existing data explodes.
Railroad carA railroad car, railcar (American and Canadian English), railway wagon, railway carriage, railway truck, railwagon, railcarriage or railtruck (British English and UIC), also called a train car, train wagon, train carriage or train truck, is a vehicle used for the carrying of cargo or passengers on a rail transport network (a railroad/railway). Such cars, when coupled together and hauled by one or more locomotives, form a train. Alternatively, some passenger cars are self-propelled in which case they may be either single railcars or make up multiple units.
Order topologyIn mathematics, an order topology is a certain topology that can be defined on any totally ordered set. It is a natural generalization of the topology of the real numbers to arbitrary totally ordered sets. If X is a totally ordered set, the order topology on X is generated by the subbase of "open rays" for all a, b in X. Provided X has at least two elements, this is equivalent to saying that the open intervals together with the above rays form a base for the order topology.
