Richardson's theorem

In mathematics, Richardson's theorem establishes a limit on the extent to which mathematics can demonstrate that certain expressions are equal. It states that sfor a certain fairly natural class of expressions, it is undecidable whether a particular expression E satisfies the equation E=0.

Specifically, the class of expressions for which the theorem holds is that generated by rational numbers, the number π, the number ln 2, the variable x, the operations of addition, multiplication, and composition, and the sin(), exp(), and abs() functions.

References

• Petkovšek, Marko (1996). A=B. A. K. Peters. p. 5. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
• Richardson, Daniel (1968), "Some unsolvable problems involving elementary functions of a real variable", Journal of Symbolic Logic, vol. 33, pp. 514–520.