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Mathematics LibreTexts

Book: Real Analysis (Boman & Rogers)


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The typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found in analysis.

Thumbnail:  Real number line with some constants such as \(\pi\). Image used with permission (Public Domain; User:Phrood).


  • Eugene Boman (Pennsylvania State University) and Robert Rogers (SUNY Fredonia)