Weird notions of “distance“ || Intro to Metric Spaces

Visit to get started learning STEM for free, and the first 200 people will get 20% off their annual premium subscription. Check out my MATH MERCH line in collaboration with Beautiful Equations ► Weird, funky types of distance can still be thought of as “distance“, but what actually is distance anyways? In this video we are going to introduce the big ideas of Metric Spaces. A Metric Space tries to generalize the notion of distance that we are all familiar with: straight line or Euclidean distance. We will see a couple other types of of distance such as the Manhattan distance aka the taxicab metric, as well as the Chebyshev distance which is basically how the king moves in chess. All of these are actually metrices! So what is a metric? Well it is a way of associating a distance that obeys three properties: 1) d(A,B)=0 iff A=B 2) d(A,B)=d(B,A) ie a symmetry property 3) d(A,C) less than or equal to d(A,B) d(B,C), called the triangle inequality. Metric spaces are a foundational idea in the field of mathematical analysis. 0:00 Euclidean or Straight Line Distance 0:24 Taxicab Metric 0:57 Chebyshev Metric 1:49 Formulas for the distances 4:34 Definition of Metric Spaces 7:14 Open Balls 9:31 Why care about Metric Spaces? 10:45 COURSE PLAYLISTS: ►DISCRETE MATH: ►LINEAR ALGEBRA: ►CALCULUS I: ► CALCULUS II: ►MULTIVARIABLE CALCULUS (Calc III): ►VECTOR CALCULUS (Calc IV) ►DIFFERENTIAL EQUATIONS: ►LAPLACE TRANSFORM: ►GAME THEORY: OTHER PLAYLISTS: ► Learning Math Series ►Cool Math Series: BECOME A MEMBER: ►Join: SOCIALS: ►Twitter (math based): ►Instagram (photography based):