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U3-1
Here are some sets:
(1) R both and
(2) ∅ both and
(3) (1,+∞) open set
(4) [−1,0] closed set, -1 and 0 , which are not interior points, belong to the set.
(5) {1,2,3} none of them is interior point. They are isolated points. And the set is discrete set. closed set
(6) {y|y=2*x^2+1,x∈[0,2)} =[1,+∞) closed set =[1,9), cuz 9 is a boundary point and is not included.
(7) Q × neither open set nor closed set
(8) Qc × neither open set nor closed set
Among the above sets, the total number of open set is: 3
the total number of closed set is: 5 4
U3-2
Consider the set S=[1,2)?{0}
Which of the following statements about S are TRUE?
Given a set S ⊂ R, a point l ∈ R is called a limit point £4Å:§ or point of accumulation(‡:) of the set S, if every deleted δ-neighborhood of l contains one or more points of S.
U4-2
Given the set of numbers S={1,1.1,0.9,1.01,0.99,1.001,0.999,...}
S={1}?{1+0.1n|n∈N}?{1−0.1n|n∈N}
∀a∈S,a≤1.1anda≥0.9
∀b<1.1,1.1∈S>b
∀c>0.9,0.9∈S<c
So 1.1 is the LUB of S, and 0.9 is the GLB of S.
∀ε>0,∃n∈N, s.t.1+0.1^n∈S and 1+0.1^n−1=0.1^n<ε 1的任意去心邻域和S的交集不为空
So 1 is a limit point of S.
U5-2
Given following numbers:
e,
π,
0,
(√3−√2)/(√3+√2), = 5 - 2 √ 6 ==> x^2 - 10 x + 1 = 0
√2+√3+√5, 可构造出6次整数系数方程的解是√2+√3+√5
2+3i, x^2 - 4 x +13 = 0
4/7
Of all the numbers above,
Which ones are algebraics?
0, 4/7
Which ones are transcendentals?
e, π,
Which ones are irrational numbers?
e, π, (√3−√2)/(√3+√2), √2+√3+√5
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原文地址：http://www.cnblogs.com/yehjianshi/p/5240335.html
