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This is a list of limits for common functions such as elementary functions. In this article, the terms a , b and c are constants with respect to x . Limits for general functions
This article is a list of notable unsolved problems in computer science. A problem in computer science is considered unsolved when no solution is known or when experts in the field disagree about proposed solutions.
By Rice's theorem, it is impossible to write a program that automatically verifies for the absence of bugs in other programs, taking a program and a specification as input, and checking whether the program satisfies the specification. This does not imply an impossibility to prevent certain types of bugs.
The Bekenstein bound limits the amount of information that can be stored within a spherical volume to the entropy of a black hole with the same surface area. Thermodynamics limit the data storage of a system based on its energy, number of particles and particle modes. In practice, it is a stronger bound than the Bekenstein bound.
The Apple "goto fail" bug was a duplicated line of code which caused a public key certificate check to pass a test incorrectly. The GnuTLS "goto fail" bug was similar to the Apple bug and found about two weeks later. The GnuTLS bug also allowed attackers to bypass SSL/TLS security. [8]
Probably the most interesting part of this theorem is that the Cauchy condition implies the existence of the limit: this is indeed related to the completeness of the real line. The Cauchy criterion can be generalized to a variety of situations, which can all be loosely summarized as "a vanishing oscillation condition is equivalent to convergence".
In computer programming, bounds checking is any method of detecting whether a variable is within some bounds before it is used. It is usually used to ensure that a number fits into a given type (range checking), or that a variable being used as an array index is within the bounds of the array (index checking).
Limits can be difficult to compute. There exist limit expressions whose modulus of convergence is undecidable. In recursion theory, the limit lemma proves that it is possible to encode undecidable problems using limits. [14] There are several theorems or tests that indicate whether the limit exists. These are known as convergence tests.