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How do you define a metric space through the use of sets?
The concept of a distance, or metric, between the elements of a set is well defined in topology. Let B be any set with x, y, z Є B, and let D be a function from the Cartesian product, B X B, into the set of real numbers, R. D is called a metric on B if the following four statements hold:1) D(x,y) ≥ 0 for all x, y2) D(x,y) = D(y,x) for all x, y3) D(x,y) = 0 if and only if x = yfor all x, y4) D(x,y) + D(y,z) ≥ D(x,z) for all x, y, zIn this case, the set B having metric D is called a metric space, and is often notated as B, D.For more information and related definitions, see the links below.
What is the solution to the equation 0 equals r?
r=0 is the solution...
18-6r equals 0 What does r equal?
Divide both sides by 6: 3 - r = 0, so r = 3 satisfies the equation.
What is the value of R in R squared -16 equals 0?
R2 - 16 = 0 R2 = 16 Take the square root of each side to get rid of the square on R. R = 4
A c program to find maximum number in a 3 by 3 matrix?
int matrix[][]; // the matrix to find the max in int max = matrix[0][0]; int r,c; for(r = 0; r < 3; ++r) { for(c = 0; c < 3; ++c) { if(matrix[r][c] > max) { max = matrix[r][c]; } } } // max is now the maximum number in matrix
In R with discrete metric space what is open set?
any interval subset of R is open and closed
What does RO2 equals stand for?
R=0 where Rici curvature tensor=0 Einstein states that Rici tensor is identically 0 which probably means space-time is non curved
What has the author James R Smart written?
James R. Smart has written: 'New understanding in arithmetic' -- subject(s): Arithmetic 'Metric math' -- subject(s): Metric system
How many 0 is there in 1 liter?
None. The only 6 characters (excluding the space) are {1,l,i,t,r,e}.
R² plus r-20 equals 0?
r2 + r - 20 = 0(r + 5)(r - 4) = 0r + 5 = 0 or r - 4 = 0r = -5 or r = 4
Space words that start with R?
a space word for R could be Rhea the moon of saturn.
How do you define a metric space through the use of sets?
The concept of a distance, or metric, between the elements of a set is well defined in topology. Let B be any set with x, y, z Є B, and let D be a function from the Cartesian product, B X B, into the set of real numbers, R. D is called a metric on B if the following four statements hold:1) D(x,y) ≥ 0 for all x, y2) D(x,y) = D(y,x) for all x, y3) D(x,y) = 0 if and only if x = yfor all x, y4) D(x,y) + D(y,z) ≥ D(x,z) for all x, y, zIn this case, the set B having metric D is called a metric space, and is often notated as B, D.For more information and related definitions, see the links below.
What is the center of blackhole?
The centre of a black hole is singularity.A singularity is NOT a (specific) place. It is a property of a function where the value of that function approaches infinity. For example, the function f: x ⟼ 1/x has a singularity at x = 0 because lim_{x → 0⁺} f(x) = +∞.A singularity is the set of points where a metric is undefined. It is a geometric property of a manifold that is not limited to black holes, and is not necessarily a single point.A singularity can be just a coordinate singularity that disappears if you choose a different coordinate system for the manifold. For example, the Schwarzschild metric that describes non-rotating electrically neutral black holes has a coordinate singularity at the event horizon in Schwarzschild coordinates, but not in Kruskal–Szekeres coordinates.By contrast, every known black hole metric has a true (curvature) singularity with all coordinate systems in or near the center of a black hole.That singularity does not need to be a point either. For example, in the Kerr and Kerr–Newman metrics that describe rotating black holes (with angular momentum J ≠ 0) the singularity is a ring (a set of adjacent points/events).Also, it is important to understand that singularities with black holes are not (a set of) points in space, but in space*time*: they are a set of *events*.A spacetime singularity does not have to be a spacetime *curvature* singularity. For example, the Schwarzschild metric, the spacetime metric of a spherical mass distribution with total mass M, zero angular momentum, and zero electric charge, has a singularity at the Schwarzschild radius r = rₛ := 2 G M/c²:ds² = ±(1 − rₛ/r) c²dt² ∓ 1/(1 − rₛ/r) dr² ∓ r² (dθ² + sin²θ dφ²).Because r = rₛ ⇒ 1/(1 − rₛ/r) = 1/0 ⇒ lim_{r → rₛ} ds² = ∓∞.However, this is NOT a spacetime *curvature* singularity because it can be avoided by using a different coordinate system. For example, the metric is in Kruskal–Szekeres coordinates:ds² = 32G³M³/r exp(−r/(2 G M)) (±dT² ∓ dX²) ∓ r² (dθ² + sin²θ dφ²),where c = 1. Now,r = rₛ = 2 G M/c² ⇒ ds² = 16G²M² exp(−1) (±dT² ∓ dX²) ∓ 4G²M² (dθ² + sin²θ dφ²) ≠ ±∞,and the spacetime singularity at r = rₛ disappears.There is still a spacetime *curvature* singularity at r = 0 because 32G³M³/0 is not defined in these coordinates, and there are no known coordinates that can avoid that.Finally, even a spacetime *curvature* singularity does NOT have to be point-like. The curvature singularity of the Kerr and Kerr–Newman metrics, for a black hole with non-zero angular momentum, is *ring*-shaped.
What is another term for the singularity or area of infinite density?
A singularity is NOT a (specific) place. It is a property of a function where the value of that function approaches infinity. For example, the function f: x ⟼ 1/x has a singularity at x = 0 because lim_{x → 0⁺} f(x) = +∞.A singularity is the set of points where a metric is undefined. It is a geometric property of a manifold that is not limited to black holes, and is not necessarily a single point.A singularity can be just a coordinate singularity that disappears if you choose a different coordinate system for the manifold. For example, the Schwarzschild metric that describes non-rotating electrically neutral black holes has a coordinate singularity at the event horizon in Schwarzschild coordinates, but not in Kruskal–Szekeres coordinates.By contrast, every known black hole metric has a true (curvature) singularity with all coordinate systems in or near the center of a black hole.That singularity does not need to be a point either. For example, in the Kerr and Kerr–Newman metrics that describe rotating black holes (with angular momentum J ≠ 0) the singularity is a ring (a set of adjacent points/events).Also, it is important to understand that singularities with black holes are not (a set of) points in space, but in space*time*: they are a set of *events*.A spacetime singularity does not have to be a spacetime *curvature* singularity. For example, the Schwarzschild metric, the spacetime metric of a spherical mass distribution with total mass M, zero angular momentum, and zero electric charge, has a singularity at the Schwarzschild radius r = rₛ := 2 G M/c²:ds² = ±(1 − rₛ/r) c²dt² ∓ 1/(1 − rₛ/r) dr² ∓ r² (dθ² + sin²θ dφ²).Because r = rₛ ⇒ 1/(1 − rₛ/r) = 1/0 ⇒ lim_{r → rₛ} ds² = ∓∞.However, this is NOT a spacetime *curvature* singularity because it can be avoided by using a different coordinate system. For example, the metric is in Kruskal–Szekeres coordinates:ds² = 32G³M³/r exp(−r/(2 G M)) (±dT² ∓ dX²) ∓ r² (dθ² + sin²θ dφ²),where c = 1. Now,r = rₛ = 2 G M/c² ⇒ ds² = 16G²M² exp(−1) (±dT² ∓ dX²) ∓ 4G²M² (dθ² + sin²θ dφ²) ≠ ±∞,and the spacetime singularity at r = rₛ disappears.There is still a spacetime *curvature* singularity at r = 0 because 32G³M³/0 is not defined in these coordinates, and there are no known coordinates that can avoid that.Finally, even a spacetime *curvature* singularity does NOT have to be point-like. The curvature singularity of the Kerr and Kerr–Newman metrics, for a black hole with non-zero angular momentum, is *ring*-shaped.
What is the solution to the equation 0 equals r?
r=0 is the solution...
Find the possible value or values of r in the quadratic equation r2 -7r - 8 0?
I think you mean r2 -7r -8 = 0. If so, then factor it: (r+1)(r-8) = 0 Then set r+1 = 0, r+1-1=-1, r = -1 Set r-8 =0, r-8+8 = 8 so r = 8
What is 46 in binary?
It is 48/2= 24 r 0 ^ 24/2= 12 r 0 | 12/2 = 6 r 0 | 6/2 = 3 r 0 | 3/2 = 1 r 1 | 1/2 = 0 r 1 | So your read it from 1 to 48 :D Enjoy
