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USING MATHEMATICAL CONVENTIONS
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The concepts for this exercise are summarized below.
For a complete discussion, read the text.
(Click here for solutions to the text exercises.)
Recall:
ℝ
is the set of real numbers:
ℝ=(-
∞,∞)
ℤ
is the set of integers:
ℤ={...
,-3,-2
,-1,0,
1,2,3,
...}
Numbers are usually represented by lowercase letters, like
a,
n, or
x .
Sets are usually represented by uppercase letters, like
A,
B, or
S .
A variable with universal set
ℝ
(or, any interval of real numbers)
is most likely to be named with a lowercase letter from the end of the alphabet;
particularly
t,
x, or
y .
A variable with universal set
ℤ
(or, any subset of the integers)
is most likely to be named with a lowercase letter near the middle of the alphabet;
particularly
i,
j,
k,
m, or
n .
EXAMPLES:
What is the best variable to represent a number, with universal set
ℝ ?
Choices:
x,
j, or
S
Answer:
x
What is the best variable to represent a member of the set [-1,3) ?
Choices:
B,
k, or
t
Answer:
t
What is the best variable to represent a set?
Choices:
t,
A, or
m
Answer:
A
What is the best variable to represent a member of the set
{3,4,
5,...} ?
Choices:
k,
S, or
y
Answer:
k