Real-Analysis
Math
Real Analysis Differential Geometry Linear Algebra Topology Set Theory General Concepts Bijective Function Injective Function Surjective Function Transitive …
Read →Surjective Function
A function is surjective or “onto” if For every \(y \in Y\), there exists \(x \in X\) such that \(f(x) = y\).
Read →Peano Axioms
A natural number is any element of the set \(\mathbb{N} = \{0, 1, 2, 3…\}\) I 0 is a natural number. II If \(n\) is a natural number, then n++ is also a …
Read →Injective Function
A function is injective (“one-to-one”) if \(x \neq x^{\prime} \Longrightarrow f(x) \neq f(x^{\prime})\) i.e. Given a set \(X\) and a set \(Y\), no …
Read →Cartesian Product
If \(X\) and \(Y\) are sets, then we define the Cartesian Product \(X \times Y\) to be the collection of ordered pairs, e.g. \((x, y)\), whose first component …
Read →Bijective Function
A function is bijective or “invertible” if it is Both one-to-one and onto (injective and surjective) In other words: each element of one set is …
Read →