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The above definition of a function is essentially that of the founders of calculus, Leibniz, Newton and Euler. However, it cannot be formalized, since there is no mathematical definition of an "assignment". It is only at the end of the 19th century that the first formal definition of a function could be provided, in terms of set theory.
3. Between two groups, may mean that the first one is a proper subgroup of the second one. > (greater-than sign) 1. Strict inequality between two numbers; means and is read as "greater than". 2. Commonly used for denoting any strict order. 3. Between two groups, may mean that the second one is a proper subgroup of the first one. ≤ 1.
Function is not the same as purpose in the teleological sense, that is, possessing conscious mental intention to achieve a goal. In the philosophy of biology, evolution is a blind process which has no 'goal' for the future. For example, a tree does not grow flowers for any purpose, but does so simply because it has evolved to do so.
This glossary of biology terms is a list of definitions of fundamental terms and concepts used in biology, the study of life and of living organisms.It is intended as introductory material for novices; for more specific and technical definitions from sub-disciplines and related fields, see Glossary of cell biology, Glossary of genetics, Glossary of evolutionary biology, Glossary of ecology ...
In the context of limits, this is shorthand meaning for sufficiently large arguments; the relevant argument(s) are implicit in the context. As an example, the function log(log(x)) eventually becomes larger than 100"; in this context, "eventually" means "for sufficiently large x." factor through
in functional programming, a pure function is idempotent if it is idempotent in the mathematical sense given in the definition. This is a very useful property in many situations, as it means that an operation can be repeated or retried as often as necessary without causing unintended effects.
For a mathematical function of a real variable, a measurement of the sensitivity to change of the function value (output) with respect to a change in its argument (input); e.g. the derivative of the position of a moving object with respect to time is the object's velocity and measures how quickly the position of the object changes as time changes.
Function (biology), the effect of an activity or process; Function (engineering), a specific action that a system can perform; Function (language), a way of achieving an aim using language; Function (mathematics), a relation that associates an input to a single output; Function (sociology), an activity's role in society