REVIEW for EXAM 2
Question 1
How can a set have no elements in it? Choose the BEST response.
a. The set of students who fail to attend class, do not do homework, and still earn an A in this
course is the empty set.
b. Think of my favorite flavors of ice-c
HOMEWORK 14
Question 1
Gloria Marie has submitted five recipies to her church's cookbook committee. She anxiously
awaits the news as to whether the committee will choose none, one, several, or all of her recipes.
How many different decisions can the commi
Course Syllabus Math 1100 (The Nature of Mathematics) Louisiana State University-Baton Rouge Instructor: Robert Perlis Lockett Hall 212 Tel: (225) 578-1673 Email: perlis@math.lsu.edu Office Hours: Daily 11:30AM-12:30PM or by appointment. Welcome to M
Subtracting sets
Lets talk about football tickets.
Let S denote the set of all season ticket holders
(student and non-student), and
let T be the set of all LSU students.
The set of season ticket holders who are NOT
LSU students is written S\T.
u ThissetS\
Counting on Fingers
Begin by labeling your fingers as follows.
128
64
32
16
8
4
256
2
512
1
The individual fingers show the powers of 2. Two show
the number 3, hold up the fingers labeled 1 and 2
together. Use your fingers to show the numbers 1, 2,
3, 4,
SizeMatters
Atapartywithlotsofpeople
standingandlotsofchairs
scatteredabout,howcanyou
tellwhethertherearemore
n
Youcouldcountthepeople,countthe
chairs,andcomparethenumbers.
n
n
Youcouldcountthepeople,countthe
chairs,andcomparethenumbers.
Youcouldaskeveryo
Pythagoras Discovery of the Irrational
Pythagoras
We have learned that between any two rational
We
numbers there is another rational number. In
fact, the half-way point between any two
rationals is another rational. As a result, if we
put a dot on the num
The Joy of Sets
What traits do men like in women?
Or women in men?
Or men in men?
Here are the results of a study of college students.
Traits M liked in W
Traits W liked in M
[Mw]
[Wm]
Beauty
Cheerfulness
Cheerfulness
Consideration
Congeniality
Intelligen
Writing Fractions as Decimals
Since Pythagoras discovered that
2 is not rational, people began to
wonder what these irrational
numbers looked like. How can we
describe them all? What is their
relationship to the rational
numbers?
By the process of long di
When I think of Infinity, I think
of.
something that goes on and on.
Acircle(nobeginning,noend.)
neverending
Lambchop,fromtheShariLewis
TVshow.Italwaysendedwith
TheSongthatNeverEnds
Thisisthesongthatneverends,yesit
goesonandonmyfriend.Somepeople
startedsi
MATH 1100
TEACHER: Dr. Perlis
How to Ace this Course
Attend every class
Do HW three times a week
Ask questions
Getting Started
I will lay cards out according to a rule.
Try to guess my rule.
Possible Rule:
Alternate Red and Black
Lets try another one:
Gue
A counting problem
How many subsets does a set A have?
A set A with 1 element looks like
A=cfw_a.
Then cfw_a is a subset (it is the biggest subset).
And there is the empty subset cfw_ .
So a set A with |A|=1 has 2 subsets.
Let A be a set of cardinality 2.
HOMEWORK 18
Question 1
How many even whole numbers are there from 4 to 1004, counting 4 and 1004?
a. 1000. Just subtract 4 from 1004.
b. 1001. Just subtract 4 from 1004, then add 1 because that's what we did in class.
c. 500. Subtract 4 from 1004 to get 1
HOMEWORK 16
Question 1
Write the sum 16x16 + 13X16 + 12 in hex notation
a. 1DC_hex
b. 1CD_hex
c. 1CD_bin
d. 1DC_bin
Correct-A
Question 2
Write the binary numberr 11110_bin in hex notation.
a. 11110_bin = 16 + 8 + 4 + 2 = 16 + 14 = 1E_hex
b. Sometimes witc
HOMEWORK 15
Question 1
Write the sum 4+8+16+32+64 in binary.
a. 1111100_bin
b. 10000000_bin
c. 124
d. There is a formula for this, but I forgot it.
Correct
Question 2
You hear Juliet counting out loud: one, two three, four, five, . .
In which base is she
HOMEWORK 13
Question 1
Exactly 15 committees can be formed from a group of people. How many people are in the
group?
a. 15
b. 15-1 = 14
c. 4
d. 3
Correct-C
Question 2
Starting from your little finger on your right hand and ending with your little finger o
HOMEWORK 12
Question 1
Create a one-to-one correspondence between the set N = cfw_1,2,3,4,5,. of all natural numbers to
the set S = cfw_2,3,4,5,6,. of all natural numbers that are 2 or larger.
a. It can't be done, since S is a proper subset of N, meaning
HOMEWORK 11
Question 1
Big Boss discovers that she can form exactly 15 different committees from her employees. How
many employees does she have?
a. 2
b. 3
c. 4
d. 5
Correct- C
Question 2
Six people are at a meeting. How many committees can be formed from
Cantors Proof that |R|s|N|
Cantor gave a wonderfully simple reason why
there cannot be a one-to-one correspondence
between N and R. It goes like this:
Suppose someonelets call him Mr. Smith
says he has found a one-to-one
correspondence between N and R. We