Mathematics

# Minkowski’s inequality

Table of Contents

## Minkowski’s inequality

## How do you prove Minkowski’s inequality?

**The triangle inequality for the ?p-norm**is called Minkowski’s inequality. It is straightforward to verify if p = 1 or p = ?, but it is not obvious if 1 <p< ?.

## Which of the following is the Minkowski inequality?

Minkowski’s integral inequality

with obvious modifications in the case p = ?. If p > 1, and both sides are finite, then equality holds only if **|F(x, y)| = ?(x)?(y) a.e.** for some non-negative measurable functions ? and ?.

## How do you prove triangle inequalities?

## What is the triangle inequality theorem in geometry?

triangle inequality, in Euclidean geometry, theorem that

**the sum of any two sides of a triangle is greater than or equal to the third side**; in symbols, a + b ? c. In essence, the theorem states that the shortest distance between two points is a straight line.## What is Minkowski inequality in metric space?

**The triangle inequality for the ?p-norm**is called Minkowski’s inequality. It is straightforward to verify if p = 1 or p = ?, but it is not obvious if 1 <p< ?.

## What does equality and inequality mean?

**the condition of being unequal; lack of equality; disparity**: inequality of size. social or economic disparity: inequality between the rich and the poor; widening income inequality in America. unequal opportunity or treatment resulting from this disparity: inequality in healthcare and education.

## How do you use Holder’s inequality?

## How do you prove a triangle is a triangle?

## What is four triangle inequality theorem?

According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.

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Triangle Inequality Theorem Proof.

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Triangle Inequality Theorem Proof.

S.No | Statement | Reason |
---|---|---|

4. | ?ADB<?DBC | ?ADB is an isosceles triangle and ?ADB = ?DBA |

5. | |BC|<|CD| | Side opposite to greater angle is larger |

## What is triangle sum theorem?

Theorem:

**The sum of the measures of the interior angles of a triangle is 180**.## What is the relationship between triangle sides and angles?

Relationship between sides and angles. In any triangle,

**the largest side and largest angle are opposite one another**. In any triangle, the smallest side and smallest angle are opposite one another. In any triangle, the mid-sized side and mid-sized angle are opposite one another.## How do you prove an open ball is an open set?

An open ball in a metric space (X, ?) is an open set. Proof.

**If x ? Br(?) then ?(x, ?) = r ? ? where ? > 0**.## What words describe inequality?

**inequality**

- bias.
- difference.
- discrimination.
- disparity.
- diversity.
- injustice.
- unfairness.
- asperity.

## What are some examples of inequalities?

The major examples of social inequality include

**income gap, gender inequality, health care, and social class**. In health care, some individuals receive better and more professional care compared to others.## How do you write an inequality?

## What is SSS SAS ASA AAS?

SSS (side-side-side) All three corresponding sides are congruent. SAS (side-angle-side) Two sides and the angle between them are congruent. ASA (angle-side-angle)

## How do you do congruency?

**For two triangles to be congruent, one of 4 criteria need to be met.**

- The three sides are equal (SSS: side, side, side)
- Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
- Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

## How do you do basic triangle proofs?

## What is triangle inequality theorem 2?

**The sum of the lengths of any two sides of a triangle is greater than the length of the third side**.

## What are the six theorems on triangle inequalities?

**Triangle Inequality Proof**

- Since the sum of any two sides is greater than the third, then the difference of any two sides will be less than the third.
- The sum of any two sides must be greater than the third side.
- The side opposite to a larger angle is the longest side in the triangle.

## Can a triangle be constructed with sides of lengths 6cm 7cm and 14cm?

6+7< 14. Since the sum of the sides of 6 cm and 7 cm is not greater than the third side of 14 cm, this given triangle is

**not possible**to construct.## What is the 3rd Angle Theorem?

The Third Angle Theorem states that

**if two angles in one triangle are congruent to two angles in another triangle, then the third pair of angles must also congruent**.## How is the triangle sum theorem used in real life?

How is the Triangular Sum Theorem Used in Real Life? A good example of the Triangular Sum Theorem would be

**when constructing a house**. The roofs of houses are often formed as a triangle. To get the measurements, you must know the degrees of all three interior angles.