Homework Answers
We know that Least Upper bound axiom means a ordered set S in wich for every nonempty subset A which is bounded above then supA i.e least upper bound of A exists in set S.
But Q not satisfy this axiom.
Because observe the following subset
A={x€Q /x²<2}
Then clearly A is nonempty bounded subset of Q
Because it is bounded by all elements x€Q and x²>2
Now we observe that SupA=√2= square root of 2
But we know that √2=square root of 2 does not belong to Q
Since it is one irrational number
So clearly supA does belong to Q
I. E Q has no least upper bound property
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4. For the following sets determine the least upper bound (it is not necessary to prove...
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not necessary
to prove that it is the least upper bound):
a.) M = [0; 1] [ (3; 4)
b.) M =
n5n + 1
4n ? 3
n 2 N
o
c.) M =
n n + 1
2n + 13
n 2 N
o
d.) M =
nXn
i=1
9
10i
n 2 N
o
e.) M =
n
xjx > 0 and x2 < 5g:...
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4. For the following sets determine the least upper bound (it is
not necessary
to prove that it is the least upper bound):
a.) M = [0; 1] [ (3; 4)
b.) M =
n5n + 1
4n ? 3
n 2 N
o
c.) M =
n n + 1
2n + 13
n 2 N
o
d.) M =
nXn
i=1
9
10i
n 2 N
o
e.) M =
n
xjx > 0 and x2 < 5g:...
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