| Symbol |
Description |
Location |
| \(\to\) |
conditional statement |
Beginning Activity |
| \(\R\) |
set of real numbers |
Subsection |
| \(\Q\) |
set of rational numbers |
Subsection |
| \(\Z\) |
set of integers |
Subsection |
| \(\wedge\) |
conjunction |
Item a |
| \(\vee\) |
disjunction |
Item b |
| \(\mynot\) |
negation |
Item c |
| \(\leftrightarrow\) |
biconditional statement |
Subsection |
| \(\equiv\) |
logically equivalent |
Definition |
| \(\N\) |
set of natural numbers |
Beginning Activity |
| \(y \in A\) |
\(y\) is an element of \(A\)
|
Item 2.13:1 |
| \(z \notin A\) |
\(z\) is not an element of \(A\)
|
Item 2.13:2 |
| \(A = B\) |
\(A\) equals \(B\) (set equality) |
Definition |
| \(A \subseteq B\) |
\(A\) is a subset of \(B\)
|
Definition |
| \(\{ \mid \}\) |
set builder notation |
Subsection |
| \(\emptyset\) |
the empty set |
Subsection |
| \(\forall\) |
universal quantifier |
Definition |
| \(\exists\) |
existential quantifier |
Definition |
| \(m \mid n\) |
\(m\) divides \(n\)
|
Definition |
| \(a \equiv b \pmod n\) |
\(a\) is congruent to \(b\) modulo \(n\)
|
Definition |
| \(\left| x \right|\) |
absolute value of \(x\)
|
Definition |
| \(n!\) |
\(n\) factorial |
Definition |
| \(f_1, f_2, f_3, \ldots\) |
Fibonacci numbers |
Beginning Activity |
| \(A \cap B\) |
intersection of \(A\) and \(B\)
|
Definition |
| \(A \cup B\) |
union of \(A\) and \(B\)
|
Definition |
| \(A^c\) |
complement of \(A\)
|
Definition |
| \(A - B\) |
set difference of \(A\) and \(B\)
|
Definition |
| \(A \not \subseteq B\) |
\(A\) is not a subset of \(B\)
|
Subsection |
| \(A \subset B\) |
\(A\) is a proper subset of \(B\)
|
Definition |
| \(\mathcal(P)( A )\) |
power set of \(A\)
|
Definition |
| \(\left| A \right|\) |
cardinality of a finite set \(A\)
|
Definition |
| \(( {a,b} )\) |
ordered pair |
Definition |
| \(A \times B\) |
Cartesian product of \(A\) and \(B\)
|
Definition |
| \(\mathbb{R} \times \mathbb{R}\) |
Cartesian plane |
Subsection |
| \(\R^2\) |
Cartesian plane |
Subsection |
| \(\bigcup\limits_{X \in \mathscr{C}}^{}X\) |
union of a family of sets |
Definition |
| \(\bigcap\limits_{X \in \mathscr{C}}^{}X\) |
intersection of a family of sets |
Definition |
| \(\bigcup\limits_{j=1}^{n}A_j\) |
union of a finite family of sets |
Subsection |
| \(\bigcap\limits_{j=1}^{n}A_j\) |
intersection of a finite family of sets |
Subsection |
| \(\bigcup\limits_{j=1}^{\infty}B_j\) |
union of an infinite family of sets |
Subsection |
| \(\bigcap\limits_{j=1}^{\infty}B_j\) |
intersection of an infinite family of sets |
Subsection |
| \(\left\{ A_\alpha \mid \alpha \in \Lambda \right\}\) |
indexed family of sets |
Definition |
| \(\bigcup\limits_{\alpha \in \Lambda}^{}A_\alpha\) |
union of an indexed family of sets |
Definition |
| \(\bigcap\limits_{\alpha \in \Lambda}^{}A_\alpha\) |
intersection of an indexed family of sets |
Definition |
| \(s ( n )\) |
sum of the divisors of \(n\)
|
Exercise 2 |
| \(f:A \to B\) |
function from \(A\) to \(B\)
|
Paragraphs |
| \(\text{ dom} ( f )\) |
domain of the function \(f\)
|
Definition |
| \(\text{ codom} ( f )\) |
codmain of the function \(f\)
|
Definition |
| \(f( x )\) |
image of \(x\) under \(f\)
|
Definition |
| \(\text{ range} ( f )\) |
range of the function \(f\)
|
Definition |
| \(d( n )\) |
number of divisors of \(n\)
|
Exercise 6 |
| \(R_n\) |
\(R_n = \{0, 1, 2, \ldots, n-1 \}\) |
Subsection |
| \(I_A\) |
identity function on the set \(A\)
|
Progress Check 6.11 |
| \(p_1, p_2\) |
projection functions |
Exercise 5 |
| \(\det ( A )\) |
determinant of \(A\)
|
Exercise 9 |
| \(A^T\) |
transpose of \(A\)
|
Exercise 10 |
| \(\det :M_{2, 2} \to \mathbb{R}\) |
determinant function |
Activity 37 |
| \(g \circ f:A \to C\) |
composition of functions \(f\) and \(g\)
|
Definition |
| \(f^{ -1 }\) |
the inverse of the function \(f\)
|
Definition |
| \(\text{Sin } ^{-1}\) |
the inverse sine function |
Activity 41 |
| \(\text{Sin}\) |
the restricted sine function |
Activity 41 |
| \(f ( A )\) |
image of \(A\) under the function \(f\)
|
Definition |
| \(f^{-1} ( C )\) |
pre-image of \(C\) under the function \(f\)
|
Definition |
| \(\text{ dom} ( R )\) |
domain of the relation \(R\)
|
Definition |
| \(\text{ range} ( R )\) |
range of the relation \(R\)
|
Definition |
| \(x \mathrel{R} y\) |
\(x\) is related to \(y\)
|
Subsection |
| \(x \mathrel{\not \negthickspace R} y\) |
\(x\) is not related to \(y\)
|
Subsection |
| \(x \sim y\) |
\(x\) is related to \(y\)
|
Subsection |
| \(x \nsim y\) |
\(x\) is not related to \(y\)
|
Subsection |
| \(R^{-1}\) |
the inverse of the relation \(R\)
|
Definition |
| \(\left[ a \right]\) |
equivalence class of \(a\)
|
Definition |
| \(\left[ a \right]\) |
congruence class of \(a\)
|
Definition |
| \(\Z_{n}\) |
the integers modulo \(n\)
|
Definition |
| \(\left[ a \right] \oplus \left[ c \right]\) |
addition in \(\mathbb{Z}_n\)
|
Definition |
| \(\left[ a \right] \odot \left[ c \right]\) |
multiplication in \(\mathbb{Z}_n\)
|
Definition |
| \(\gcd ( {a, b} )\) |
greatest common divisor of \(a\) and \(b\)
|
Definition |
| \(A \approx B\) |
\(A\) is equivalent to \(B\text{,}\) \(A\) and \(B\) have the same cardinality |
Definition |
| \(\N_k\) |
\(\mathbb{N}_k = \left\{ 1, 2, \ldots, k \right\}\) |
Subsection |
| \(\text{ card} ( A ) = k\) |
cardinality of \(A\) is \(k\)
|
Definition |
| \(\aleph_0\) |
cardinality of \(\mathbb{N}\)
|
Definition |
| \(\boldsymbol{c}\) |
cardinal number of the continuum |
Definition |