Synonyymit & Tietoja | englanti sana INFINITE

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Esimerkkejä INFINITE käyttämisestä lauseessa

• Informally put, the axiom of choice says that given any collection of sets, each containing at least one element, it is possible to construct a new set by choosing one element from each set, even if the collection is infinite.
• Similarly, the set of algebraic (real) numbers is countably infinite and has Lebesgue measure zero as a subset of the real numbers, and in that sense, almost all real numbers are transcendental.
• Throughout mathematics, "almost all" is sometimes used to mean "all (elements of an infinite set) except for finitely many".
• In his 1619 book Harmonices Mundi, Johannes Kepler observed the existence of the infinite family of antiprisms.
• With the axiom of dependent choice (which is a weakened form of the axiom of choice), this result can be reversed: if there are no such infinite sequences, then the axiom of regularity is true.
• For instance, the field of all algebraic numbers is an infinite algebraic extension of the rational numbers.
• The absolute infinite (symbol: Ω), in context often called "absolute", is an extension of the idea of infinity proposed by mathematician Georg Cantor.
• In mathematics, specifically set theory, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets.
• Equivalently, a set is countable if there exists an injective function from it into the natural numbers; this means that each element in the set may be associated to a unique natural number, or that the elements of the set can be counted one at a time, although the counting may never finish due to an infinite number of elements.
• One such generalization is that a topological space is sequentially compact if every infinite sequence of points sampled from the space has an infinite subsequence that converges to some point of the space.
• A fundamental theorem due to Georg Cantor shows that it is possible for infinite sets to have different cardinalities, and in particular the cardinality of the set of real numbers is greater than the cardinality of the set of natural numbers.
• Beginning in the late 19th century, this concept was generalized to infinite sets, which allows one to distinguish between different types of infinity, and to perform arithmetic on them.
• In mathematics, the classification of finite simple groups is a result of group theory stating that every finite simple group is either cyclic, or alternating, or belongs to a broad infinite class called the groups of Lie type, or else it is one of twenty-six exceptions, called sporadic (the Tits group is sometimes regarded as a sporadic group because it is not strictly a group of Lie type, in which case there would be 27 sporadic groups).
• It has low (ideally zero) resistance in one direction and high (ideally infinite) resistance in the other.
• It can be used to approximate integrals by finite sums, or conversely to evaluate finite sums and infinite series using integrals and the machinery of calculus.
• Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous than the natural numbers.
• In mathematics, a geometric series is a series summing the terms of an infinite geometric sequence, in which the ratio of consecutive terms is constant.
• A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.
• Various traditions describe the Holy Grail as a cup, dish, or stone with miraculous healing powers, sometimes providing eternal youth or sustenance in infinite abundance, often guarded in the custody of the Fisher King and located in the hidden Grail castle.
• Human languages possess the properties of productivity and displacement, which enable the creation of an infinite number of sentences, and the ability to refer to objects, events, and ideas that are not immediately present in the discourse.
• In the hypothetical case that the universe is static, homogeneous at a large scale, and populated by an infinite number of stars, any line of sight from Earth must end at the surface of a star and hence the night sky should be completely illuminated and very bright.
• Formal theories cannot dispense with primitive notions, under pain of infinite regress (per the regress problem).
• Cantor's diagonal argument shows that the power set of a set (whether infinite or not) always has strictly higher cardinality than the set itself (or informally, the power set must be larger than the original set).
• In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes the movement of a free particle in a small space surrounded by impenetrable barriers.
• For an example of an infinite abelian p-group, see Prüfer group, and for an example of an infinite simple p-group, see Tarski monster group.

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