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In mathematics, and especially in category theory, a commutative diagram is a diagram of objects, also known as vertices, and morphisms, also known as arrows or edges, such that when selecting two objects any directed path through the diagram leads to the same result by composition.
In mathematical logic, it remains used for denoting implication, but its exact meaning depends on the specific theory that is studied. 4. Over a variable name , means that the variable represents a vector , in a context where ordinary variables represent scalars ; for example, v → {\displaystyle {\overrightarrow {v}}} .
Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
A chart of all prime knots with seven or fewer crossings, not including mirror-images. The knots are labeled with Alexander-Briggs notation . Originally studied to create a list of possible real-world knots, knot theory has become quite theoretical in nature and, at the same time, has been applied to concrete problems in organic chemistry ...
A nomogram (from Greek νόμος (nomos) 'law' and γράμμα 'that which is drawn'), also called a nomograph, alignment chart, or abac, is a graphical calculating device, a two-dimensional diagram designed to allow the approximate graphical computation of a mathematical function.
In mathematics, particularly homological algebra, an exact functor is a functor that preserves short exact sequences. Exact functors are convenient for algebraic calculations because they can be directly applied to presentations of objects.
In mathematics, for a function :, the image of an input value is the single output value produced by when passed . The preimage of an output value y {\displaystyle y} is the set of input values that produce y {\displaystyle y} .
The United States Naval Observatory states "the Equation of Time is the difference apparent solar time minus mean solar time", i.e. if the sun is ahead of the clock the sign is positive, and if the clock is ahead of the sun the sign is negative. [6] [7] The equation of time is shown in the upper graph above for a period of slightly more than a ...