## Properties of Real Functions

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## 1.**Definition**: Continuous Functions at Single Real Numbers

## 2.**Definition**: Continuous Real Functions

## 3.**Definition**: Monotonic Functions

## 4.**Definition**: Bounded and Unbounded Functions

## 5.Differentiable Functions

## 6.**Definition**: Continuously Differentiable Functions

## 7.**Definition**: Uniformly Continuous Functions (Real Case)

## 8.**Definition**: Periodic Functions

## 9.**Definition**: Even and Odd Functions

## 10.Integrable Functions

## 11.**Lemma**: Invertible Functions on Real Intervals

## 12.**Definition**: Convex and Concave Functions

## 13.**Definition**: Logarithmically Convex and Concave Functions

## 14.Uniform Convergence of Functions