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Faithfulness means unfailingly remaining loyal to someone or something, and putting that loyalty into consistent practice regardless of extenuating circumstances. It may be exhibited, for example, by a husband or wife who does not engage in sexual relationships outside of the marriage . [ 1 ]
In mathematics, especially in an area of abstract algebra known as representation theory, a faithful representation ρ of a group G on a vector space V is a linear representation in which different elements g of G are represented by distinct linear mappings ρ(g).
A faithful functor need not be injective on objects or morphisms. That is, two objects X and X′ may map to the same object in D (which is why the range of a full and faithful functor is not necessarily isomorphic to C), and two morphisms f : X → Y and f′ : X′ → Y′ (with different domains/codomains) may map to the same morphism in D.
Fides (Latin: Fidēs) was the goddess of trust, faithfulness, and good faith in ancient Roman religion. [1] [2] Fides was one of the original virtues to be cultivated as a divinity with ceremonies and temples. [3] Fides Publica holding a cornucopia and extending a libation bowl on the reverse of a dupondius issued by Vespasian 77–78 AD
There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics).
The mathematics portal is a good "way in" to mathematics articles on Wikipedia. If you are in doubt, ask at the mathematics reference desk. No one on Wikipedia is going to do your math homework for you, but if you ask the right question they might point you to some information that will enable you to do it for yourself.
The SAT Subject Test in Mathematics Level 2 covered more advanced content. Generally you need to have completed a semester of a pre-calculus class with a solid “B” or better to feel comfortable on the Math 1, whereas the content of the Math 2 test extends through Algebra II and basic trigonometry, precalculus, and basic calculus.
Informally, a field is a set, along with two operations defined on that set: an addition operation written as a + b, and a multiplication operation written as a ⋅ b, both of which behave similarly as they behave for rational numbers and real numbers, including the existence of an additive inverse −a for all elements a, and of a multiplicative inverse b −1 for every nonzero element b.