Verify that the discrete metric is actually a metric.

Q: Exercise. Show that in R with the euclidean metric, any subset of R\Q with more than one element is…

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Q: Prove that any contraction between metric spaces has at most one fixed point

A: According to the given information, it is required to prove that any contraction between metric…

Q: Find all limit points of a set B = {1, }, , 1,...} on the real line with the usual metric. Is B open…

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Q: Let X and Y be two compact spaces, show that X × Y is compact

A: It suffices if we show there is a collection of open sets that covers X×Y. Let U be an open cover of…

Q: Every totally  bounded metric space is compact

A: This statement is not always true.

Q: If X =R and d(x.y)30, then X metric space not metric semi metric

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Q: State whether the following is true or false: a) The set [0,4] with the usual metric is…

A: (a) The set [0,4] with the usual metric is sequentially compact. This statement is true. Considering…

Q: メ=D¢ c omplex number %3D Doyou CGid) is metric space of not ??

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Q: Exercise 4. If d is a metric on the set X, we define dcut : X × X → [0, 1] by dcut (x, y) = min(d(x,…

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Q: Let d be a metric on X + 0. Show that the function e defined by d(a, b) 1+ d(a, b) e(a, b) = %3D…

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Q: Find the orthogonal compliment to S span{ 0 }. ||

A: To find the orthogonal complement to S spanned by two vectors .

Q: Consider ℝ3 with the metric d((x1, x2, x3), (y1, y2, y3) = |x1 - y1| + |x2 - y2| + |x3 - y3|. i.…

A: Given metric is          d((x1, x2, x3), (y1, y2, y3)) = |x1 - y1| + |x2 - y2| + |x3 - y3|.   For…

Q: The curvature of any line with slope m in 2-space at any point on it is TTL

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Q: Show that d(x y) = √x-y defines a metric on the set of all real numbers

A: We will use the basic knowledge of metric spaces and set theory to answer this question.

Q: Define metric space and define its four properties

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Q: . Prove or disprove every metric space is normed space,

A: A normed vector space or normed space is a vector space over the real or complex numbers, on which a…

Q: Show that the real line is a metric space.

A: Answer is mentioned below

Q: The set [0, 1] with the discrete metric is compact. True False

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Q: Define the term dimension of a space.

A: In mathematics, the dimension of space means the minimum number of coordinated to specify or located…

Q: Exercise. Every point in a discrete metric space forms an open ball.

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Q: Show that: All completions of a metric space are isometric.

A: According to the given information, it is required to show that all the completions of a metric…

Q: A metric space (X,d) such that the function d1(p, q) = (d(p, q)) i not a metric in X

A: Since (X, d) is a metric space. So, d is a function defined as d : X×X→R+∪0 and satisfy the…

Q: What is the dimension of the vector space P°?

A: The dimension of Pn is n+1

Q: Find all limit points of a set A = {(2+,2 – |n e N} on the Euclidean plane with the isual metric. Is…

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Q: Assume the distance metric is Euclidean, what is the Y-coordinate value for the FIRST iteration of…

A: From the given information, Location Coordinate(xi) Coordinate(yi) Weight(Wi) 1 2…

Q: Verify the discrete metric d2 satises the triangle inequality.

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Q: Show that ℓ^1 is a normed linear space.

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Q: Every point in a discrete metric space forms an open ball.

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Q: Suppose E ⊂ Real Numbers. With respect to the Euclidean metric, is it possible that E' = { 1/n: n ∈…

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Q: 2.5 Show that any interval (a,b) inR with the discrete metric is locally compact but not compact.

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Q: The set R- {0} with the usual metric is connected.

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Q: Is it possible to have a function on a metric space which is discontimuous at every point of the…

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Q: Define new metric which is different from giving in above questions on X in question 01.

A: With the help of questions 01 we define a new metric on X

Q: The set [0,4] with the usual metric is sequentially compact. O True O False

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Q: d(x,y) 1 - Y -

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Q: Is the set S = [0,1] with the discrete metric d separable? Explain

A: We Know that a set is separable in metric space only if it contains a countable dense subset in it.…

Q: Please do no 3 for me using definition of Metric spaces

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Q: What is Euclidean Space??

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Q: Find all limit points of a set A = {(2+,2 – 1)|n e N} on the Euclidean plane with the usual metric.…

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Q: Exercise.3 Show that the following the functions d and p on X = R? are metrics or not, such that 2.…

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Q: What is Sierpinski Space? Also give example

A: Sierpinski Space is  a topological space. Now to define a topological space we have to define a…

Q: Show that by using an example that every metric is a pesudo metric but converse is not true.

A: To show that every metric is a pesudo metric but converse is not true.

Q: Show that the Euclidean metric is a metric( i.e. verify that the function d satisfies the three…

A: Here we have to show thatt Euclidean metric is a metric.

Q: What is the dimension of the vector space R

A: The objective is to find the dimension of the vector space R5.

Q: (a) Consider the metric space 0 (i) if r 1.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: not vector spaces

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Q: the function d satisfies the three condition in the definitión of metric on page 39). 3. Show that…

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Q: (X,d) be a metric space. Define f: X x X -> Real Numbers by f(x,y) = d(x,y) / 1+d(x,y) . show that f…

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Q: Exercise 1.33. Let (X,d) be a metric spáce and d(x,y) 1+d(x,y)' d* (x,y) = Prove that the family of…

A: This is problem from my old works, where I used e instead of d*.

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.