prove that d (x1,xn)<=d (x1,x2)+d (x2,x3)+.................+d (xn-1,xn)
One metric ton is equivalent to 1,000 kilograms. The volume of space occupied by one metric ton of materials will vary depending on the density of the substance. For example, one metric ton of lead will take up less space than one metric ton of feathers due to their different densities.
Matter is defined as that which has mass and occupies space. There are procedures to measure both. Even if you can't measure the mass of an object directly (such as a gas), you can still determine it's mass by measuring the space it occupies. Pressure is one way to measure the mass of gas by the amount of space it occupies.
A solid is more compact.
The basic metric for liquid is volume, which is typically measured in units such as liters (L) or milliliters (mL). This measurement indicates the amount of space that the liquid occupies.
That depends on what substance the dealer has a metric ton of. If it's a metric ton of air, the price is probably quite low, although they would probably not offer to deliver it. It it's a metric ton of water, the price is probably a bit higher, but still quite low, and they might include delivery. If it's a metric ton of gold, I would expect the price to be very high; but it would be rather compact, and whatever quantity you buy would probably fit easily in the back seat of your car.
No.
A metric on a set is complete if every Cauchy sequence in the corresponding metric space they form converges to a point of the set in question. The metric space itself is called a complete metric space. See related links for more information.
Any closed bounded subset of a metric space is compact.
The question doesn't make sense, or alternatively it is true by definition. A Hilbert Space is a complete inner product space - complete in the metric induced by the norm defined by the inner product over the space. In other words an inner product space is a vector space with an inner product defined on it. An inner product then defines a norm on the space, and every norm on a space induces a metric. A Hilbert Space is thus also a complete metric space, simply where the metric is induced by the inner product.
The assumptions of a metric space except for symmetry.
The assumptions of a metric space except for symmetry.
You can find a compact parking space for your vehicle in parking lots, garages, or on the street in designated compact car spaces.
The metric space ( \mathbb{R} \setminus {0} ) is not complete because there exist Cauchy sequences in this space that do not converge to a limit within the space. For instance, consider the sequence ( x_n = \frac{1}{n} ), which is a Cauchy sequence in ( \mathbb{R} \setminus {0} ) since it approaches 0 as ( n ) goes to infinity. However, the limit of this sequence, 0, is not included in ( \mathbb{R} \setminus {0} ), demonstrating that the space lacks completeness.
The determinant of the metric in a space determines the properties of that space, such as its curvature and distance measurements. It helps define the geometry and structure of the space.
When looking for a small range hood for a compact kitchen space, consider features like efficient ventilation power, compact size to fit the space, adjustable fan speeds, and easy-to-clean filters.
I am also dying to know geometrical interpretation of semi-metric space . If anyone have idea please do infrom me as well
large population and lack of space in the cities, the settlement is compact