# Category:Continuous Real Functions

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This category contains results about **Continuous Real Functions**.

Definitions specific to this category can be found in Definitions/Continuous Real Functions.

The concept of **continuity** makes precise the intuitive notion that a function has no "jumps" or "holes" at a given point.

Loosely speaking, a real function $f$ is **continuous** at a point $p$ if and only if the graph of $f$ does not have a "break" at $p$.

## Subcategories

This category has the following 16 subcategories, out of 16 total.

## Pages in category "Continuous Real Functions"

The following 45 pages are in this category, out of 45 total.

### A

### C

- Combination Theorem for Continuous Functions/Real
- Combination Theorem for Continuous Real Functions
- Composite of Continuous Mappings is Continuous/Corollary
- Concave Real Function is Continuous
- Constant Function is Continuous/Real Function
- Constant Real Function is Continuous
- Continuous at Point iff Left-Continuous and Right-Continuous
- Continuous Function is not necessarily Differentiable
- Continuous Function on Closed Real Interval is Uniformly Continuous
- Continuous Real Function has Riemann Integral
- Continuous Real Function is Darboux Integrable
- Continuous Real Function on Closed Interval is Bijective iff Strictly Monotone
- Convex Real Function is Continuous

### E

### L

### M

### R

- Real Elementary Functions are Continuous
- Real Exponential Function is Continuous
- Real Logarithm Function is Continuous
- Real Natural Logarithm Function is Continuous
- Real Polynomial Function is Continuous
- Real Power Function for Positive Integer Power is Continuous
- Real Rational Function is Continuous
- Real Trigonometric Functions are Continuous
- Right-Hand Differentiable Function is Right-Continuous
- Rolle's Theorem