We are planning to prepare a Glossary for the course that contains a list of the key terms that are used in the course.
Which terms would you like us to explain here?
\(:=\) Equal by definition. E.g., for any real number \(a\in \mathbb R\) one has \(a^2:= a\cdot a\).
\(\exists\) :There exists.
\(\in\): Belongs to
\(\subset\): Is a subset of
\(\cup\): Union of sets
\(\cap\): Intersection of sets
\(\forall\): For every
\(\mathbb N\): The set of natural numbers \(0,1,2,3,…\).
\(\mathbb Q\): The set of rational numbers.
\(\mathbb R\): The set of real numbers.
\(\mathbb Z\): The set of integer numbers \(…,-3,-2,-1,0, 1,2,3,…\): \(\mathbb N\subset\mathbb Z\subset\mathbb Q\subset\mathbb R\)
Integer: a number of the set \(\mathbb Z=\lbrace …,-3,-2,-1,0,1,2,3,…\rbrace\)
Natural number: a number of the set \(\mathbb N=\lbrace 0,1,2,3,…\rbrace\)
Rational number: a number of the set \(\mathbb Q=\left\lbrace \dfrac ab:\, a\in\mathbb Z, b\in\mathbb Z\setminus\lbrace 0\rbrace\right\rbrace=\left\lbrace \dfrac ab:\, a\in\mathbb Z, b\in\mathbb N\setminus\lbrace 0\rbrace\right\rbrace\)
Real number: an element of \(\mathbb R\). The set \(\mathbb R\) contains the limits of sequences of rational numbers and elements like square roots, \(\pi, e,…\)
Square root of \(x\ge 0\): the positive number \(y\) satisfying \(y^2=x\).
\(m-\)th root of \(x\ge 0\): the positive number \(y\) satisfying \(y^m=x\).