7 List of the used symbols

The table below is compatible with the notation used in the lectures and exercises of BIE-ZMA.

Symbol Meaning
\(=\) symbol of equality
\(:=\) equality by definition, the expression on the left is defined on the right
\(a \leq b\) \(a\) is less than or equal to \(b\)
\(a \geq b\) \(a\) is greater than or equal to \(b\)
\(a < b\) \(a\) is less than \(b\)
\(a > b\) \(a\) is greater than \(b\)
\(\N = \{1,2,\ldots\}\) set of natural numbers
\(\N_0 = \{0,1,2,\ldots\}\) set of natural number plus \(0\)
\(\Z\) set of integer numbers
\(\Q\) set of rational numbers
\(\R\) set of real numbers
\(\CC\) set of complex numbers
\(\Re z\) real part of the complex number \(z\)
\(\Im z\) imaginary part of the complex number \(z\)
\((a,b)\) open interval, or an ordered pair or point in a plane
\([ a,b ]\) closed interval
\(A \subset B\) \(A\) is a subset of \(B\), it admits \(A = B\)
\(A \cup B\) union of the sets \(A\) and \(B\)
\(A \cap B\) intersection of the sets \(A\) and \(B\)
\(A \smallsetminus B\) set difference
\(A \times B\) Cartesian product of the sets \(A\) and \(B\)
\(|A|\) number of elements of the set \(A\)
\(x \in A\) \(x\) is an element of the set \(A\)
\(x \notin A\) \(x\) is not an element of the set \(A\)
\(\wedge\) conjunction
\(\vee\) disjunction
\(\Rightarrow\) implication
\(\Leftrightarrow\) equivalence
\(\forall\) universal quantifier
\(\exists\) existential quantifier
\(D_f\) nebo \(D(f)\) domain of a function \(f\)
\(H_f\) nebo \(H(f)\) image set of a function \(f\)
\(\ee\) Euler’s number
\(\pi\) Ludolph’s number
\(\ii\) imaginary unit
\(\sin\) function sine
\(\cos\) function cosine
\(\tg\) function tangent
\(\ctg\) function cotangent
\(\arcsin\) function arcsine
\(\arccos\) function arccosine
\(\arctg\) function arctangent
\(\log_a\) logarithm of base \(a\), \(0 < a \neq 1\)
\(\ln\) natural logarithm, i.e. \(\log_\ee\)
\(\log\) decimal logarithm, i.e. \(\log_{10}\)
\(\lfloor x \rfloor\) lower integer part of the real number \(x\)
\(\lceil x \rceil\) upper integer part of the real number \(x\)
\(|x|\) absolute value of the number \(x\)
\(n!\) factorial of the number \(n\)
\(\binom{n}{k}\) binomial coefficient

The following table lists frequently used Greek letters with their name.

Greek letter Upper case Name LaTeX
\(\alpha\) alpha alpha
\(\beta\) beta beta
\(\gamma\) \(\Gamma\) gamma gamma
\(\delta\) \(\Delta\) delta delta
\(\epsilon\) epsilon epsilon
\(\zeta\) zeta zeta
\(\eta\) eta eta
\(\theta\) \(\Theta\) theta theta
\(\kappa\) kappa kappa
\(\lambda\) \(\Lambda\) lambda lambda
\(\mu\) mu mu
\(\nu\) nu nu
\(\xi\) \(\Xi\) xi xi
\(\pi\) \(\Pi\) pi pi
\(\rho\) rho rho
\(\sigma\) \(\Sigma\) sigma sigma
\(\tau\) tau tau
\(\varphi\) \(\Phi\) phi varphi
\(\chi\) chi chi
\(\psi\) \(\Psi\) psi psi
\(\omega\) \(\Omega\) omega omega