The list of elements from A = { − 8 , − 2 3 , − 6 , 0 , 4 5 , 9 , 10. 6 ¯ } that belong to natural numbers.

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Answer 1

Question

Chapter 6, Problem 1CRE

(a)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to natural numbers.

(b)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to whole numbers.

(c)

To determine

To calculate: The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to integers.

(d)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to rational numbers.

(e)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to irrational numbers.

(f)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to real numbers.

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Q1lal Let X be an arbitrary infinite set and let r the family of all subsets F of X which do not contain a particular point x, EX and the complements F of all finite subsets F of X show that (X.r) is a topology. bl The nbhd system N(x) at x in a topological space X has the following properties NO- N(x) for any xX N1- If N EN(x) then x€N N2- If NEN(x), NCM then MeN(x) N3- If NEN(x), MEN(x) then NOMEN(x) N4- If N = N(x) then 3M = N(x) such that MCN then MeN(y) for any уем Show that there exist a unique topology τ on X. Q2\a\let (X,r) be the topology space and BST show that ẞ is base for a topology on X iff for any G open set xEG then there exist A Eẞ such that x E ACG. b\Let ẞ is a collection of open sets in X show that is base for a topology on X iff for each xex the collection B, (BEB\xEB) is is a nbhd base at x. - Q31 Choose only two: al Let A be a subspace of a space X show that FCA is closed iff F KOA, K is closed set in X. الرياضيات b\ Let X and Y be two topological space and f:X -…

Q1\ Let X be a topological space and let Int be the interior operation defined on P(X) such that 1₁.Int(X) = X 12. Int (A) CA for each A = P(X) 13. Int (int (A) = Int (A) for each A = P(X) 14. Int (An B) = Int(A) n Int (B) for each A, B = P(X) 15. A is open iff Int (A) = A Show that there exist a unique topology T on X. Q2\ Let X be a topological space and suppose that a nbhd base has been fixed at each x E X and A SCX show that A open iff A contains a basic nbdh of each its point Q3\ Let X be a topological space and and A CX show that A closed set iff every limit point of A is in A. A'S A ACA Q4\ If ẞ is a collection of open sets in X show that ẞ is a base for a topology on X iff for each x E X then ẞx = {BE B|x E B} is a nbhd base at x. Q5\ If A subspace of a topological space X, if x Є A show that V is nbhd of x in A iff V = Un A where U is nbdh of x in X.

Answer 2

Question

Chapter 6, Problem 1CRE

(a)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to natural numbers.

(b)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to whole numbers.

(c)

To determine

To calculate: The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to integers.

(d)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to rational numbers.

(e)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to irrational numbers.

(f)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to real numbers.

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Answer 3

Question

Chapter 6, Problem 1CRE

(a)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to natural numbers.

(b)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to whole numbers.

(c)

To determine

To calculate: The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to integers.

(d)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to rational numbers.

(e)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to irrational numbers.

(f)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to real numbers.

Expert Solution & Answer

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Answer 4

Question

Chapter 6, Problem 1CRE

(a)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to natural numbers.

(b)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to whole numbers.

(c)

To determine

To calculate: The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to integers.

(d)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to rational numbers.

(e)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to irrational numbers.

(f)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to real numbers.

Expert Solution & Answer

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Answer 5

Chapter 6, Problem 1CRE

(a)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to natural numbers.

(b)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to whole numbers.

(c)

To determine

To calculate: The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to integers.

(d)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to rational numbers.

(e)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to irrational numbers.

(f)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to real numbers.

Answer 6

Chapter 6, Problem 1CRE

(a)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to natural numbers.

Answer 7

Chapter 6, Problem 1CRE

(a)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to natural numbers.

Answer 8

(b)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to whole numbers.

Answer 9

(b)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to whole numbers.

Answer 10

(c)

To determine

To calculate: The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to integers.

Answer 11

(c)

To determine

To calculate: The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to integers.

Answer 12

(d)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to rational numbers.

Answer 13

(d)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to rational numbers.

Answer 14

(e)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to irrational numbers.

Answer 15

(e)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to irrational numbers.

Answer 16

(f)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to real numbers.

Answer 17

(f)

To determine

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to real numbers.

Answer 18

Expert Solution & Answer

Answer 19

Expert Solution & Answer

Answer 20

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Answer 21

Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Concept Check Work each problem. Which two of the...Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

The list of elements from A = { − 8 , − 2 3 , − 6 , 0 , 4 5 , 9 , 10. 6 ¯ } that belong to natural numbers.

Solution Summary: The author analyzes the list of elements from A=left-8,-23,-sqrt6.

Concept explainers

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to natural numbers.

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to whole numbers.

To calculate: The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to integers.

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to rational numbers.

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to irrational numbers.

The list of elements from A={−8,−23,−6,0,45,9,10.6¯} that belong to real numbers.

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Chapter 6 Solutions