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HOMEWORK 1
0. Email me with:
•
Your full name (as it appears in Bearfacts).
•
The email address where you’d prefer to receive class announcements.
•
Your student number.
•
I will hold oﬃce hours during 3 of the following 6 time slots: Mon 121, Tue 121,
Wed 121, Thu 121, Fri 1011, Fri 1112. Let me know which of these you will
be able to attend, and I will try to accommodate everyone if possible.
•
23 sentences about your major, why you’re taking this course, and what you
hope to gain from it.
•
23 sentences of something interesting  a fact about yourself, random trivia, etc.
1. Let
f
:
X
→
X
be a function. Recall that we deﬁned
f
n
:
X
→
X
by
f
n
(
x
) =
f
(
f
(
...
(
f

{z
}
n
times
(
x
))
...
)). Prove that if
f
is surjective, then
f
n
is surjective for all
n
.
2. Prove by induction that for any set
X
, if
X
is ﬁnite, then
P
(
X
)

= 2

X

.
3. Recall that if
z
=
a
+
bi
∈
C
, then its
complex conjugate
, denoted
z
*
, is
a

bi
. Also,
its
magnitude
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This note was uploaded on 03/28/2012 for the course MATH 110 taught by Professor Gurevitch during the Fall '08 term at Berkeley.
 Fall '08
 GUREVITCH
 Math

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