# Continuous function

### 1817

In contrast, the function denoting the amount of money in a bank account at time would be considered discontinuous, since it "jumps" at each point in time when money is deposited or withdrawn. ==History== A form of the epsilon–delta definition of continuity was first given by Bernard Bolzano in 1817.

### 1830

The formal definition and the distinction between pointwise continuity and uniform continuity were first given by Bolzano in the 1830s but the work wasn't published until the 1930s.

### 1854

Eduard Heine provided the first published definition of uniform continuity in 1872, but based these ideas on lectures given by Peter Gustav Lejeune Dirichlet in 1854. ==Real functions== ===Definition=== A real function, that is a function from real numbers to real numbers, can be represented by a graph in the Cartesian plane; such a function is continuous if, roughly speaking, the graph is a single unbroken curve whose domain is the entire real line.

### 1872

Eduard Heine provided the first published definition of uniform continuity in 1872, but based these ideas on lectures given by Peter Gustav Lejeune Dirichlet in 1854. ==Real functions== ===Definition=== A real function, that is a function from real numbers to real numbers, can be represented by a graph in the Cartesian plane; such a function is continuous if, roughly speaking, the graph is a single unbroken curve whose domain is the entire real line.

### 1930

The formal definition and the distinction between pointwise continuity and uniform continuity were first given by Bolzano in the 1830s but the work wasn't published until the 1930s.

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