The Fundamental Theorems of Interval Analysis
<|reference_start|>The Fundamental Theorems of Interval Analysis: Expressions are not functions. Confusing the two concepts or failing to define the function that is computed by an expression weakens the rigour of interval arithmetic. We give such a definition and continue with the required re-statements and proofs of the fundamental theorems of interval arithmetic and interval analysis.   Revision Feb. 10, 2009: added reference to and acknowledgement of P. Taylor.<|reference_end|>
@article{van emden2007the,
    title={The Fundamental Theorems of Interval Analysis},
    author={M.H. van Emden and B. Moa},
    journal={arXiv preprint arXiv:cs/0701141},
    year={2007},
    number={DCS-316-IR},
    archivePrefix={arXiv},
    eprint={cs/0701141},
    primaryClass={cs.NA}
}