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Appendix A Notation
| Symbol |
Description |
Location |
| \(\therefore\) |
therefore |
Assemblage |
| \(\neg p\) |
not \(p\text{;}\) negation |
Item |
| \(p\wedge q\) |
\(p\) and \(q\text{;}\) conjunction |
Item |
| \(p\vee q\) |
\(p\) or \(q\text{;}\) disjunction (inclusive) |
Item |
| \(p\veebar q\) |
\(p\) exclusive or \(q\text{;}\) disjunction (exclusive) |
Item |
| \(p\rightarrow q\) |
if \(p\) then \(q\text{;}\) conditional |
Item |
| \(p\leftrightarrow q\) |
\(p\) if and only if \(q\text{;}\) biconditional |
Item |
| \(p // q\) |
\(p\) nand \(q\text{;}\) not both |
Item |
| \(\mathbb{t}\) |
tautology; always true |
Paragraph |
| \(\mathbb{c}\) |
contradiction; always false |
Paragraph |
| \(P\equiv Q\) |
\(P\) is logically equivalent to \(Q\)
|
Definition 1.3.14 |
| \(x\in S\) |
\(x\) is an element of set \(S\)
|
Paragraph |
| \(x\notin S\) |
\(x\) is not an element of set \(S\)
|
Paragraph |
| \(B\subseteq A\) |
\(B\) is a subset of \(A\)
|
Paragraph |
| \(B\nsubseteq A\) |
\(B\) is not a subset of \(A\)
|
Paragraph |
| \(\mathbb{R}\) |
the set of real numbers |
Item |
| \(\mathbb{Z}\) |
the set of integers |
Item |
| \(\mathbb{Q}\) |
the set of rational numbers |
Item |
| \(\mathbb{N}\) |
the set of natural numbers |
Item |
| \(\mathbb{Z}^+\) |
the set of positive integers |
Item |
| \(\mathbb{Z}^{nonneg}\) |
the set of nonnegative integers |
Item |
| \(\mathbb{R}^{+}\) |
the set of positive real numbers |
Item |
| \(\mathbb{R}^{nonneg}\) |
the set of nonnegative real numbers |
Item |
| \(\emptyset\) |
empty set; set with no elements |
Paragraph |
| \(\forall\) |
for all; universal quantifier |
Item |
| \(\exists\) |
there exists; existential quantifier |
Item |
| \(\mathbb{R}\setminus\mathbb{Q}\) |
the set of irrational numbers |
Definition 3.2.2 |
| \(d\mid n\) |
\(d\) divides \(n\)
|
Paragraph |
| \(\sum_{k=1}^{n}a_k\) |
the sum \(a_1+a_2+\cdots +a_n\)
|
Assemblage |
| \(\prod_{k=1}^{n}a_k\) |
the product \(a_1\cdot a_2\cdot a_3\cdots a_n\)
|
Paragraph |
| \(n!\) |
\(n\) factorial; \((n)(n-1)\cdots(2)(1)\)
|
Paragraph |
| \(A\cup B\) |
the union of \(A\) and \(B\)
|
Paragraph |
| \(A\cap B\) |
the intersection of \(A\) and \(B\)
|
Paragraph |
| \(A-B\) |
the set difference \(A\) minus \(B\)
|
Paragraph |
| \(A\setminus B\) |
the set difference \(A\) minus \(B\)
|
Paragraph |
| \(A^C\) |
the complement of \(A\)
|
Paragraph |
| \(\mathcal{P}(A)\) |
The power set of \(A\)
|
Definition 5.2.9 |
| \(A\times B\) |
the Cartesian product of \(A\) and \(B\)
|
Paragraph |
| \(x R y\) |
\(x\) is related to \(y\)
|
Paragraph |
| \(m\equiv n \mod d\) |
\(m\) is congruent to \(n\) mod \(d\)
|
Definition 5.4.11 |
| \([a]\) |
the equivalence class of \(a\)
|
Paragraph |
| \(\binom{n}{r}\) |
\(n\) choose \(r\text{;}\) binomial coefficient |
Definition 6.1.1 |
| \(|A|\) |
cardinality of set \(A\)
|
Paragraph |
