injection

injection, introduction of a fluid into the body, usually by means of a needle and syringe. The material injected may be a test substance (as in determining allergic sensitivity or immunity to a disease), an anesthetic, a therapeutic drug, a nutrient (in cases where intravenous feeding is necessary), blood, or blood plasma (see blood transfusion). An intracutaneous injection is the introduction of a small amount of fluid between the skin layers. A subcutaneous injection is directed to the tissues under the skin. When quicker absorption of a drug is required, an intramuscular injection may be used; even more rapid action is obtained by injection into a vein (intravenous). In certain emergencies involving the heart, such as cardiac arrest, an intracardiac injection can penetrate directly into a chamber of the musculature of the heart. Anesthetics are sometimes injected into the spine. In an injection by means of a jet injector gun, fluid penetrates through the skin by means of air pressure and there is no visible puncture mark. Micro-injections can be made into fetuses, even individual cells, with tiny capillary injectors.

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1.	(mathematics)	injection - A function, f : A -> B, is injective or one-one, or is an injection, if and only if for all a,b in A, f(a) = f(b) => a = b. I.e. no two different inputs give the same output (contrast many-to-one). This is sometimes called an embedding. Only injective functions have left inverses f' where f'(f(x)) = x, since if f were not an injection, there would be elements of B for which the value of f' was not unique. If an injective function is also a surjection then is it a bijection.
2.	(reduction)	injection - An injection function is one which takes objects of type T and returns objects of type C(T) where C is some type constructor. An example is f x = (x, 0). The opposite of an injection function is a projection function which extracts a component of a constructed object, e.g. fst (x,y) = x. We say that f injects its argument into the data type and fst projects it out.