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Countable , normed linear

Authored by Stephy Stephen

Mathematics

University

Used 5+ times

Countable , normed linear
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20 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Define a countable set and provide an example.

The set of all real numbers is an example of a countable set.

The set of all even numbers is an example of an uncountable set.

The set of all prime numbers is an example of a finite set.

The set of all integers is an example of a countable set.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Is the set of all integers countable or uncountable?

countable

infinite

uncountable

finite

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Identify whether the set of real numbers is countable or uncountable.

Countable

Uncountable

Finite

Infinite

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the cardinality of a countable set?

infinity (∞)

ten (10)

aleph-null (ℵ₀)

two (2)

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Provide an example of an uncountable set.

The set of all natural numbers.

The set of all real numbers.

The set of all finite strings.

The set of all integers.

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Explain the concept of Lebesgue measure in your own words.

Lebesgue measure is solely concerned with the properties of continuous functions.

Lebesgue measure is a technique for counting discrete points.

Lebesgue measure is a method for measuring the size of sets in a way that generalizes traditional notions of length, area, and volume.

Lebesgue measure only applies to finite sets.

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Calculate the Lebesgue measure of the interval [0, 1].

0.5

1

2

0

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