Speaking Mathematically
Mariusz Bajger
COMP2781/8781
School of Computer Science, Engineering and Mathematics
February 25, 2011
1 / 12
Reading and Exercises
Reading
Epp, Chapter 1
Exercises
Sec. 1 (all), Sec. 2 (all), Sec.3 (all)
Good learning strategy: BE ACTIVE!
I
Regularly revise lectures
I
Solve the suggested exercises
I
Be critical when reading textbook/lectures
I
Ask your colleagues, ask the lecturer, don’t be shy!
I
It is OK to ask for help any time
2 / 12
Mathematical Statements
Notation
R
: the set of real numbers
Z
: the set of integers
Z
+
: the set of positive integers (greater than zero)
Q
: the set of rational numbers
I
Is there
a number
±
such that 2
·
±
−
4 =
±
2
?
I
For every
integer
n
: (
n
+ 1)
2
=
n
2
+ 2
n
+ 1
I
Are there two numbers with the property that the sum of
their squares equals the square of their sums?
I
Are there two numbers
a
and
b
such that
a
2
+
b
2
= (
a
+
b
)
2
? or even better
I
Do there
exist
a
,
b
∈
R
such that
a
2
+
b
2
= (
a
+
b
)
2
I
For any
two real numbers
a
and
b
:
a
2
+
b
2
= (
a
+
b
)
2
3 / 12
Universal, Existential and Conditional
I
universal statement
says that a property is true
for all
elements
e.g. For all
n
∈
Z
:
n
2
≥
0
I
existential statement
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 Spring '08
 WOUTERS
 Math, Algebra, Set Theory, School of Computer Science, Mariusz Bajger

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