ultrametric distance - ορισμός. Τι είναι το ultrametric distance
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Τι (ποιος) είναι ultrametric distance - ορισμός

BRANCH OF NUMBER THEORY THAT DEALS WITH THE ANALYSIS OF FUNCTIONS OF P-ADIC NUMBERA
Ultrametric analysis; Ultrametric calculus; P-adic calculus

Distance         
  • The distances between these three sets do not satisfy the triangle inequality:<math display="block">d(A,B)>d(A,C)+d(C,B)</math>
  • Distance along a path compared with displacement.  The Euclidean distance is the length of the displacement vector.
  • Airline routes between [[Los Angeles]] and [[Tokyo]] approximately follow a direct [[great circle]] route (top), but use the [[jet stream]] (bottom) when heading eastwards. The shortest route appears as a curve rather than a straight line because the [[map projection]] does not scale all distances equally compared to the real spherical surface of the Earth.
  • [[Manhattan distance]] on a grid
LENGTH OF STRAIGHT LINE THAT CONNECTS TWO POINTS IN A MEASURABLE SPACE OR IN AN OBSERVABLE PHYSICAL SPACE
Distances; Distance Formula; Distance in time; Time distance; Directed distance; Distance traveled; Oriented distance; Distance (mathematics); Distance between sets
·noun Remoteness of place; a remote place.
II. Distance ·vt To place at a distance or remotely.
III. Distance ·noun Space between two antagonists in fencing.
IV. Distance ·noun Ideal disjunction; discrepancy; contrariety.
V. Distance ·noun A space marked out in the last part of a race course.
VI. Distance ·vt To cause to appear as if at a distance; to make seem remote.
VII. Distance ·noun The interval between two notes; as, the distance of a fourth or seventh.
VIII. Distance ·noun Length or interval of time; period, past or future, between two eras or events.
IX. Distance ·noun The remoteness or reserve which respect requires; hence, respect; ceremoniousness.
X. Distance ·noun A withholding of intimacy; alienation; coldness; disagreement; variance; restraint; reserve.
XI. Distance ·noun Remoteness in succession or relation; as, the distance between a descendant and his ancestor.
XII. Distance ·vt To outstrip by as much as a distance (see Distance, ·noun, 3); to leave far behind; to surpass greatly.
XIII. Distance ·noun The part of a picture which contains the representation of those objects which are the farthest away, ·esp. in a landscape.
XIV. Distance ·noun Relative space, between troops in ranks, measured from front to rear;
- contrasted with interval, which is measured from right to left.
XV. Distance ·noun The space between two objects; the length of a line, especially the shortest line joining two points or things that are separate; measure of separation in place.
distance         
  • The distances between these three sets do not satisfy the triangle inequality:<math display="block">d(A,B)>d(A,C)+d(C,B)</math>
  • Distance along a path compared with displacement.  The Euclidean distance is the length of the displacement vector.
  • Airline routes between [[Los Angeles]] and [[Tokyo]] approximately follow a direct [[great circle]] route (top), but use the [[jet stream]] (bottom) when heading eastwards. The shortest route appears as a curve rather than a straight line because the [[map projection]] does not scale all distances equally compared to the real spherical surface of the Earth.
  • [[Manhattan distance]] on a grid
LENGTH OF STRAIGHT LINE THAT CONNECTS TWO POINTS IN A MEASURABLE SPACE OR IN AN OBSERVABLE PHYSICAL SPACE
Distances; Distance Formula; Distance in time; Time distance; Directed distance; Distance traveled; Oriented distance; Distance (mathematics); Distance between sets
¦ noun
1. the length of the space between two points: I cycled the short distance home.
2. the condition of being remote.
a far-off point.
3. the full length of a race or other contest.
Brit. Horse Racing a space of more than twenty lengths between two finishers in a race.
(the distance) Brit. Horse Racing a length of 240 yards from the winning post on a racecourse.
4. an interval of time.
5. aloofness or reserve.
¦ verb make distant.
?(often distance oneself from) dissociate or separate.
Phrases
go the distance last or continue to participate until the scheduled end of a contest.
keep one's distance stay far away.
?maintain one's reserve.
Origin
ME (in the sense 'discord, debate'): from OFr. or from L. distantia, from distant-, distare (see distant).
Distance         
  • The distances between these three sets do not satisfy the triangle inequality:<math display="block">d(A,B)>d(A,C)+d(C,B)</math>
  • Distance along a path compared with displacement.  The Euclidean distance is the length of the displacement vector.
  • Airline routes between [[Los Angeles]] and [[Tokyo]] approximately follow a direct [[great circle]] route (top), but use the [[jet stream]] (bottom) when heading eastwards. The shortest route appears as a curve rather than a straight line because the [[map projection]] does not scale all distances equally compared to the real spherical surface of the Earth.
  • [[Manhattan distance]] on a grid
LENGTH OF STRAIGHT LINE THAT CONNECTS TWO POINTS IN A MEASURABLE SPACE OR IN AN OBSERVABLE PHYSICAL SPACE
Distances; Distance Formula; Distance in time; Time distance; Directed distance; Distance traveled; Oriented distance; Distance (mathematics); Distance between sets
Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.

Βικιπαίδεια

P-adic analysis

In mathematics, p-adic analysis is a branch of number theory that deals with the mathematical analysis of functions of p-adic numbers.

The theory of complex-valued numerical functions on the p-adic numbers is part of the theory of locally compact groups. The usual meaning taken for p-adic analysis is the theory of p-adic-valued functions on spaces of interest.

Applications of p-adic analysis have mainly been in number theory, where it has a significant role in diophantine geometry and diophantine approximation. Some applications have required the development of p-adic functional analysis and spectral theory. In many ways p-adic analysis is less subtle than classical analysis, since the ultrametric inequality means, for example, that convergence of infinite series of p-adic numbers is much simpler. Topological vector spaces over p-adic fields show distinctive features; for example aspects relating to convexity and the Hahn–Banach theorem are different.