## Properties of Real Functions

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

## 2.**Definition**: Monotonic Functions

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

## 4.Differentiable Functions

## 5.**Definition**: Periodic Functions

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

## 7.Integrable Functions

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

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

## 10.**Definition**: Limits of Real Functions

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