QII State whether the following statements are true or labe: 1- Le S be anon-empty subset of the set of real numbers R. if S is bounded above, then supS is exist but need not to be unique in general. 2- ifA =1-5,5) and B- (5,10), then ins (A + B) - 10 and sup(A + B) = 15.. 3- the closed interval (1,2] has no maximal clement. 4. the set of natural numbers N of R is unbounded. 5- the set of real numbers R has Sup = o und ins 6- the set 5= (x e R;x' -25 s 0) has max(S) - 5 and inf(S) = -5 with no minimal element.: -o. 7- the set S= (1+: nez*) has max(5) = 2 and Min(5) = 1. 8- every bounded set of real numbers R has maximal and minimal elements. 9- the properties (M,) and (M2) of the definition of the metric space are state that the distance from any point to another is never negative, and that the distance from appoint to itself is zero. 10- there are many metric functions d: M x M- R that can be defined on a non-emnty set M
QII State whether the following statements are true or labe: 1- Le S be anon-empty subset of the set of real numbers R. if S is bounded above, then supS is exist but need not to be unique in general. 2- ifA =1-5,5) and B- (5,10), then ins (A + B) - 10 and sup(A + B) = 15.. 3- the closed interval (1,2] has no maximal clement. 4. the set of natural numbers N of R is unbounded. 5- the set of real numbers R has Sup = o und ins 6- the set 5= (x e R;x' -25 s 0) has max(S) - 5 and inf(S) = -5 with no minimal element.: -o. 7- the set S= (1+: nez*) has max(5) = 2 and Min(5) = 1. 8- every bounded set of real numbers R has maximal and minimal elements. 9- the properties (M,) and (M2) of the definition of the metric space are state that the distance from any point to another is never negative, and that the distance from appoint to itself is zero. 10- there are many metric functions d: M x M- R that can be defined on a non-emnty set M
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![QII State whether the following statements are true or false:
1- Let S be anon-empty subset of the set of real numbers R. ifS is bounded
above, then sups is exist but need not to be unique in general.
2- ifA =(-5,5) and B - (5,10), ihen inf (A + B) = 10 and sup(A + B) =
15.,
3- the closed interval (1,2] has no maximal element.
4. the set of natural numbers N of R is unbounded. .
3- the set of real numbers R has Sup = o und inf
6- the set 5 = (x €E R;x -25 s 01 has max(S) - 5 and inf(S) = -5 with
no minimal element.:
7- the set S= (1+: nez*} has max(5) = 2 and Min(5) = 1.
8- every bounded set of real numbers R has maximal and minimal elements.
9- the properties (M,) and (M2) of the definition of the metric space are state
that the distance from any point to another is never negative, and that the
distance from appoint to itself is zero. -
there are many metric functions d: M x M - R that can be defined
on a non-empty set M.
-o,
10-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad6f39df-4740-46a5-be9c-fc1cc04b6b8e%2F497c6c1a-e5ef-4be0-b068-9737fa922cdf%2F278pey_processed.jpeg&w=3840&q=75)
Transcribed Image Text:QII State whether the following statements are true or false:
1- Let S be anon-empty subset of the set of real numbers R. ifS is bounded
above, then sups is exist but need not to be unique in general.
2- ifA =(-5,5) and B - (5,10), ihen inf (A + B) = 10 and sup(A + B) =
15.,
3- the closed interval (1,2] has no maximal element.
4. the set of natural numbers N of R is unbounded. .
3- the set of real numbers R has Sup = o und inf
6- the set 5 = (x €E R;x -25 s 01 has max(S) - 5 and inf(S) = -5 with
no minimal element.:
7- the set S= (1+: nez*} has max(5) = 2 and Min(5) = 1.
8- every bounded set of real numbers R has maximal and minimal elements.
9- the properties (M,) and (M2) of the definition of the metric space are state
that the distance from any point to another is never negative, and that the
distance from appoint to itself is zero. -
there are many metric functions d: M x M - R that can be defined
on a non-empty set M.
-o,
10-
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