- published: 04 Oct 2012
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In mathematics, a metric or distance function is a function that defines a distance between each pair of elements of a set. A set with a metric is called a metric space. A metric induces a topology on a set, but not all topologies can be generated by a metric. A topological space whose topology can be described by a metric is called metrizable.
In differential geometry, the word "metric" may refer to a bilinear form that may be defined from the tangent vectors of a differentiable manifold onto a scalar, allowing distances along curves to be determined through integration. It is more properly termed a metric tensor.
A metric on a set X is a function (called the distance function or simply distance)
where [0,∞) is the set of non-negative real numbers (because distance can't be negative so we can't use R), and for all x, y, z in X, the following conditions are satisfied:
Conditions 1 and 2 together define a positive-definite function. The first condition is implied by the others.
Metric or metrical may refer to:
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers),structure,space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.
Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.
Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.
An easy way to convert in the metric system: King Henry Died By Drinking Chocolate Milk
Metric unit conversion Watch the next lesson: https://www.khanacademy.org/math/pre-algebra/rates-and-ratios/metric-system-tutorial/v/converting-within-the-metric-system?utm_source=YT&utm;_medium=Desc&utm;_campaign=PreAlgebra Missed the previous lesson? https://www.khanacademy.org/math/pre-algebra/rates-and-ratios/unit_conversion/v/speed-translation?utm_source=YT&utm;_medium=Desc&utm;_campaign=PreAlgebra Pre-Algebra on Khan Academy: No way, this isn't your run of the mill arithmetic. This is Pre-algebra. You're about to play with the professionals. Think of pre-algebra as a runway. You're the airplane and algebra is your sunny vacation destination. Without the runway you're not going anywhere. Seriously, the foundation for all higher mathematics is laid with many of the concepts that we wil...
This is a basic introduction to the idea of a metric space. I introduce the idea of a metric and a metric space framed within the context of R^n. I show that a particular distance function satisfies the conditions of being a metric.
The metric system of measures makes conversions between them very easy, since all conversions are based on powers of ten. In this video I talk about converting centimeters to meters and back, kilometers to meters, and centimeters to millimeters. (Or, in UK English spelling, centimetres to metres and back, kilometres to metres, and centimetres to millimetres.) Most important: when working out conversions, don't talk about "moving the decimal point", but rather teach students to move the digits left or right. There is a video on this topic for students here: Watch on YouTube: http://youtu.be/JbnfU5FCkfA ► SUBSCRIBE to learn more expert tips on teaching K-6 math for understanding: http://bit.ly/2a5pUkq Dr Peter Price has been teaching primary/elementary math for over 35 years, and is ...
Metric conversions made easy when solving with dimensional analysis. Metric conversions require you to know how to convert lbs (pounds) to kg (kilograms), tsp (teaspoons) to Tbsp (tablespoons) .etc and using the formula for dimensional analysis makes solving metric conversions very easy. This tutorial shows how to solve basic conversion problems using dimensional analysis. Liters to milliliters, teaspoons to tablespoons and I show how to set-up the problems. Free Quiz on Basic Metric Conversions: http://www.registerednursern.com/dosages-calculation-conversion-quiz/ Subscribe: http://www.youtube.com/subscription_center?add_user=registerednursern Nursing School Supplies: http://www.registerednursern.com/the-ultimate-list-of-nursing-medical-supplies-and-items-a-new-nurse-student-nurse-need...
In this video, we give an introduction to metric spaces by stating the definition and drawing some pictures. In the next video, we'll look at some examples of metric spaces. Video URL: https://youtu.be/MwjjHxz3dok Channel URL: https://www.youtube.com/channel/UCtTFrEPIqaKfWyGkBi9Rmvg
Real Analysis by Prof. S.H. Kulkarni, Department of Mathematics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in
Heine-Borel Theorem, connected sets, limits in metric spaces, uniqueness of limits
Professor Encinosa reviews a quick example of calculating the terms of the metric tensor and some other properties.
Professor Encinosa reviews the introduction of the metric tensor and it's use in the framework of General Relativity.
In this talk I present two concavity assumptions on the distance. The first one is the non-negative curvature analogue of Busemann’s non-positive curvature condition and resembles a sectional curvature-like condition comparable to the measure contraction property. It holds for certain non-Riemannian Finsler manifolds, but it is not clear whether it is compatible with Ohta’s Ricci curvature on Finsler manifolds. Whenever the n-dimensional Hausdorff measure is non-trivial then the measure contraction property holds and the space is a PI-space. Independent of this one always obtains a bi-Lipschitz splitting theorem. The second condition, called uniform smoothness, is dual to uniform convexity of the distance function and gives a convex exhaustion function, a first step towards a soul theorem....
An easy, clear explanation of converting metric measurements using King Henry Died By Drinking Chocolate Milk. Please Like, Share and Subscribe. Thank you! Check out my other channel for DIY projects, experiments, and making with various materials: Vintage Wood Workshop https://www.youtube.com/user/fenderhead23
Functional Analysis by Prof. P.D. Srivastava, Department of Mathematics, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in
We see how metrics defined on sets give rise to natural topologies.
Part of Basic Instruction video series designed for Anatomy 10A students at Mt. San Antonio College in Walnut, CA. Please let me know what you think.
Real Analysis, Spring 2010, Harvey Mudd College, Professor Francis Su. Playlist, FAQ, writing handout, notes available at: http://analysisyawp.blogspot.com/
This lesson consists of providing you with a Self-Tutorial of the basic units used in measurement. These are the ones I discuss: Units of Time, Units of Length (Metric and U.S.), Units of Area (Metric and U.S.), Units of Volume (Metric and U.S.), Units of Mass (Metric and U.S.), Units of Liquid Capacity (Metric and U.S.), Units of Dry Capacity (Metric and U.S.), and other miscellaneous Units. Conversion Formulas and Abbreviations are also listed. This is a "must have" Lesson for those moving on to solving Word Problems in Algebra and other higher math.
Einstein's Field Equations for General Relativity - including the Metric Tensor, Christoffel symbols, Ricci Cuvature Tensor, Curvature Scalar, Stress Energy Momentum Tensor and Cosmological Constant.
A mini course on real analysis (by Dr. Ali Sekmen) that gives an overview of spaces including Normed Vector Spaces, Inner Product Spaces, Banach Spaces, Hilbert Spaces, Metric Spaces, and Topological Spaces. It also introduces subspaces, principle angles between subspaces, union of subspaces, intersection of subspaces, disjoint subspaces, and independent subspaces. You can find the PowerPoint slides at http://www.tnstate.edu/computer_science/datascience/mini_courses.aspx
2010 Clay Research Conference Metric Geometry and Analysis of 4-Manifold Gang Tian Clay Mathematics Institute http://www.claymath.org/video