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1. 실습한 내용
1 $\in$ $Z$.
1 in ZZ
True True |
1/2 in ZZ
False False |
1/2 in QQ
True True |
sqrt(2) in QQ
False False |
sqrt(2) in RR
True True |
2^(1/3) in RR
True True |
sqrt(4) in QQ
True True |
i^2
-1 -1 |
I in RR
False False |
I in CC
True True |
QQ(.5)
1/2 1/2 |
RR(sqrt(2))
1.41421356237310 1.41421356237310 |
(sqrt(2)).n(digits=20)
1.4142135623730950488 1.4142135623730950488 |
not True
False False |
True and False
False False |
True or False
True True |
(True or False) and False
False False |
1 == 1
True True |
not(True or False) == True and False
False False |
not (True or False) == (False and True)
True True |
1 + i >= 2 - i
(I + 1) >= (-I + 2) (I + 1) >= (-I + 2) |
((3/2) > 1) or (2/3 < 1)
True True |
((3/2) > 1) ^^ (2/3 < 1)
False False |
x=1/3
x > 1/2
False False |
t=t+1
t
9 9 |
((3/2) > 1) ^^ (2/3 < 1)
False False |
s=12;s
12 12 |
t=7
t=t+1
t
8 8 |
a,b=1,2
a
1 1 |
b
2 2 |
c,d,e=2,3,5
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c,d,e
(2, 3, 5) (2, 3, 5) |
a = b = 1
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a
1 1 |
b
1 1 |
f(x) = x^2 + x + 1
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f(2)
7 7 |
f(3)
13 13 |
[6, 28, 496, 8128]
[6, 28, 496, 8128] [6, 28, 496, 8128] |
[1..7]
[1, 2, 3, 4, 5, 6, 7] [1, 2, 3, 4, 5, 6, 7] |
[4..9]
[4, 5, 6, 7, 8, 9] [4, 5, 6, 7, 8, 9] |
[2,4..10]
[2, 4, 6, 8, 10] [2, 4, 6, 8, 10] |
[1,4..13]
[1, 4, 7, 10, 13] [1, 4, 7, 10, 13] |
[1,11..31]
[1, 11, 21, 31] [1, 11, 21, 31] |
[1,11..35]
[1, 11, 21, 31] [1, 11, 21, 31] |
[pi,4*pi..32]
[pi, 4*pi, 7*pi, 10*pi] [pi, 4*pi, 7*pi, 10*pi] |
[pi/4, pi/2..2*pi]
[1/4*pi, 1/2*pi, 3/4*pi, pi, 5/4*pi, 3/2*pi, 7/4*pi, 2*pi] [1/4*pi, 1/2*pi, 3/4*pi, pi, 5/4*pi, 3/2*pi, 7/4*pi, 2*pi] |
[sin(t) for t in [pi/4, pi/2..2*pi]]
[1/2*sqrt(2), 1, 1/2*sqrt(2), 0, -1/2*sqrt(2), -1, -1/2*sqrt(2), 0] [1/2*sqrt(2), 1, 1/2*sqrt(2), 0, -1/2*sqrt(2), -1, -1/2*sqrt(2), 0] |
A = Set([2,3,3,3,2,1,8,6,3])
A
{8, 1, 2, 3, 6}
{8, 1, 2, 3, 6}
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C = Set([sin(t) for t in [pi/4, pi/2..2*pi]])
C
{0, 1, -1/2*sqrt(2), 1/2*sqrt(2), -1}
{0, 1, -1/2*sqrt(2), 1/2*sqrt(2), -1}
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A.cardinality()
5 5 |
8 in A
True True |
B = Set([8,6,17,-4,20, -2 ])
B
{17, 20, 6, 8, -4, -2}
{17, 20, 6, 8, -4, -2}
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A.union(B).cardinality()
9 9 |
A.intersection(B).cardinality()
2 2 |
A.difference(B)
{1, 2, 3}
{1, 2, 3}
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B.difference(A)
{17, 20, -4, -2}
{17, 20, -4, -2}
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A.symmetric_difference(B)
{17, 2, 3, 20, 1, -4, -2}
{17, 2, 3, 20, 1, -4, -2}
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A = Set([1,2,3]); A
{1, 2, 3}
{1, 2, 3}
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powA = A.subsets(); powA
Subsets of {1, 2, 3}
Subsets of {1, 2, 3}
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powA.list()
[{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}]
[{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}]
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pairsA = A.subsets(2); pairsA
Subsets of {1, 2, 3} of size 2
Subsets of {1, 2, 3} of size 2
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pairsA.list()
[{1, 2}, {1, 3}, {2, 3}]
[{1, 2}, {1, 3}, {2, 3}]
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[-9, -7..30]
[-9, -7, -5, -3, -1, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29] [-9, -7, -5, -3, -1, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29] |
[-18, -15..100]
[-18, -15, -12, -9, -6, -3, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99] [-18, -15, -12, -9, -6, -3, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99] |
Set([tan(t) for t in [0, pi/4..pi]])
{0, 1, Infinity, -1}
{0, 1, Infinity, -1}
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A=Set([3, 6..20])
A
{18, 3, 6, 9, 12, 15}
{18, 3, 6, 9, 12, 15}
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powA=A.subsets()
powA.cardinality()
64 64 |
f(x)=x^2+3*x
plot(f(x), (x, -5, 5))
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f(x)=x^2+3*x
plot(f(x), (x, -5, 5))
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