Continuous Function

I've drafted an initial article on Continuous Function. Please review.

Review by Critic Carla:

The article is well-written, technically accurate, and adheres to an encyclopedic tone. The lead section is substantial, and the progression from intuitive to formal definitions is logical.

However, to meet the standards of a comprehensive Wikipedia-style entry, I suggest the following improvements:

• Expand the "Types of Continuity" section with examples: While the text explains uniform and Lipschitz continuity, the section would benefit from a dedicated subsection or a list of common examples (e.g., mentioning that $f(x) = \sin(x)$ is uniformly continuous on $\mathbb{R}$) to help the reader apply the theoretical definitions.
• Add a section on the relationship between Continuity and Differentiability: There is a critical conceptual gap regarding the fact that differentiability implies continuity, but continuity does not imply differentiability (e.g., the Weierstrass function or the absolute value function). This is a cornerstone of mathematical analysis and should be explicitly addressed.
• Improve formatting of lists: The "Formal Definitions" and "Discontinuity" sections contain fragmented HTML/formatting (multiple and tags for single items), which creates excessive whitespace. These should be consolidated into single, clean numbered or bulleted lists.
• Fill the "Notable contributors" field in the infobox: The infobox currently lists "Not specified." This should be populated with key figures such as Augustin-Louis Cauchy (who formalized the $\epsilon$-$\delta$ definition) and Karl Weierstrass.

Fact-check by Fact-Checker Finn:

• The phrase "The importance of continuity cannot be overstated" is non-neutral and promotional in tone.
• The claim that the "drawing" definition implies there are no "asymptotes within its domain" is slightly misleading; a function can have an asymptote at a point outside its domain while remaining continuous throughout its domain.
• The statement that the Intermediate Value Theorem and Extreme Value Theorem "depend entirely" on continuity is a sweeping generalization; while continuity is the standard requirement, these theorems can be generalized to other contexts (e.g., connected spaces in topology).
• The description of an "Essential Discontinuity" as occurring when the function "approaches infinity (an asymptote)" is imprecise; a pole (where the limit is infinity) is often distinguished from an essential singularity (where the limit does not exist in any sense, such as $\sin(1/x)$).

Review complete. Some issues were flagged. @Scientist Sage, please address the feedback.

Addressed feedback and improved the article. @Continuous Function has been revised.

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Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.

Feedback has been addressed by an external contributor. @Continuous Function has been revised.