deduction rules are enough to produce the consequences of any set of axioms. These rules were proved by Kurt Gödel in 1930 to be enough to produce every theorem. The actual notion of computation was isolated soon after, starting with Gödel's incompleteness theorem. This theorem showed that axiom systems were limited when reasoning about the computation that deduces their theorems. Church and Turing independently demonstrated that Hilbert's (decision problem) was unsolvable, thus identifying the computational core of the incompleteness theorem. This work, along with Gödel's work on general recursive functions, established that there are sets of simple instructions, which, when put together, are able to produce any computation. The work of Gödel showed that the notion of computation is essentially unique. In 1941 Konrad Zuse completed the Z3 computer. Zuse was not familiar with Turing's work on computability at the time. In particular, the Z3 lacked dedicated facilities for a conditional jump, thereby precluding it from being Turing complete. However, in 1998, it was shown by Rojas that the Z3 is capable of simulating conditional jumps, and therefore Turing complete in theory. To do this, its tape program would have to be long enough to execute every possible path through both sides of every branch. The first computer capable of conditional branching in practice, and therefore Turing complete in practice, was the ENIAC in 1946. Zuse's Z4 computer was operational in 1945, but it did not support conditional branching until 1950. Computability theory Computability theory uses models of computation to analyze problems and determine whether they are computable and under what circumstances. The first result of computability theory is that there exist problems for which it is impossible to predict what a (Turing-complete) system will do over an arbitrarily long time. The classic example is the halting problem: create an algorithm that takes as input a program in some Turing-complete language and some data to be fed to that program, and determines whether the program, operating on the input, will eventually stop or will continue forever. It is trivial to create an algorithm that can do this for some inputs, but impossible to do this in general. For any characteristic of the program's eventual output, it is impossible to determine whether this characteristic will hold. This impossibility poses problems when analyzing real-world computer programs. For example, one cannot write a tool that entirely protects programmers from writing infinite loops or