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

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: *5. Prove that no two lines in hyperbolic geometry are equidistant from one another by showing that…

A: To prove that no two lines in hyperbolic geometry are equidistant from one another , first we…

Q: Consider the closed rectangle R = [a,b] × [c,d] in ℝ2 (under the Euclidean metric). i. Explain why…

A: Consider the closed rectangle R = [a, b] × [c, d] in ℝ2 (under the Euclidean metric). For (i), We…

Q: If X= R and d be the discrete metric Then the set of natural number (N, d) is complete no decision…

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

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Q: Let X = [0, 1] and d be the usual metric, d(x, y) = |x- y| %3D O True O False

A: TRUE

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: Show that a set A in ℝ2 is open in the Euclidean metric ⇔ it is open in the Manhattan metric. Hint:…

A: Assume that A is open subset of R2  in an Euclidean metric. So A can be written as,…

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: Ex: Let d is a trivial metric o space ) show that every infir

A: We have given trivial metric space d on infinite set X. We have to show that every infinite subset…

Q: What is norm space

A: In mathematics, a normed space or a normed vector space is a vector space over the real or complex…

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

A: Answer is mentioned below

Q: Geometry Proof. Please write the answer like column proofs(statements and reasons), so I can…

A: Given two secants say PA and PB from an external point P are equal.

Q: Verify that the discrete metric is actually a metric.

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Q: Let two metrics be bi-lipschitz, prove it is an equivalence relation

A: Find the attachment for the solution.

Q: give example is not To-SPace about to folegical SPace

A: We have to find a topological space which is not t0.

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: Verify the discrete metric d2 satises the triangle inequality.

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Q: Suppose that point C lies in plane X and point D lies in plane X. What can you conclude regarding…

A: What can you conclude regarding CD↔.

Q: which axioms for a finite projective plane are also valid in Euclidean geometry? which are not?

A: A finite geometry is any geometric system that has only a finite number of points. The familiar…

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

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Q: The quotient topology actually defines a topology.

A: The quotient topology  actually defines a topology

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: let M= To,2] anel d be bhe usual metric then d is not compact or Compact ?

A: A set is said to be compact if and only if it is closed and bounded.

Q: The usuall metric space (Rd)isComplete ***

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Q: What are the elements of Euclidean and Non-Euclidean Geometry?

A: Solution

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

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

A: We have to decide whether the given statement is true or false.

Q: Draw the unit “circle” around the origin in the Euclidean metric, the taxicab metric, the hub…

A: The unit circle around the origin in Euclidean metric is The unit circle around the origin in…

Q: If X = {a, b} , how many metric can be de fined on X %3D infinite O none O only one O only finite

A: only one

Q: Give an example that satisfies in arbitrary metric space, boundedness and closedness do not…

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Q: What is Euclidean Space??

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Q: Show that the linear map (x, y)H (x+ y, x- y) from (R?, || - |1,) to (R?, I| - ||is an isometry.

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Q: Show that closed ball in metric space (x,d) is a closed set. Also,

A: Given: (x,d) is a metric space The objective is to show that the closed ball y in (x,d) is a closed…

Q: 3. Show that X = [0, 1] with the discrete metric is bounded but not totally bounded.

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Q: The set {0,3} with the usual metric is connected as union of connected sets {0} and {3} True False

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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: Prove analytically that in any triangle the perpendiculars drawn from the vertices upon the opposite…

A: Given-  the perpendiculars drawn from the vertices upon the opposite sides. To prove-the altitudes…

Q: If X is a metric space and Y C X, then Y is a metric space.

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Q: show that a set of natural numbers N ,with Euclidean metric is Separable

A: We have to prove that a set of natural numbers N, with Euclidean metric is Separable.

Q: Define an isometry.

A: To Define an isometry.

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

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Q: Let ū=(1,l02) and V=(-1,3,0), find the distance dlū,).

A:

Q: s the dimension of

A: Given vectors are: 0,1,2,0,0,6,1,5,3 We have to find the dimension of the above set of vectors.

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.