Editing Conjecture (section)

===Independent conjectures===
Not every conjecture ends up being proven true or false. The [[continuum hypothesis]], which tries to ascertain the relative [[cardinal number|cardinality]] of certain [[infinite set]]s, was eventually shown to be [[Independence (mathematical logic)|independent]] from the generally accepted set of [[Zermelo–Fraenkel axioms]] of set theory. It is therefore possible to adopt this statement, or its negation, as a new [[axiom]] in a consistent manner (much as [[Euclid]]'s [[parallel postulate]] can be taken either as true or false in an axiomatic system for geometry).

In this case, if a proof uses this statement, researchers will often look for a new proof that ''does not'' require the hypothesis (in the same way that it is desirable that statements in [[Euclidean geometry]] be proved using only the axioms of neutral geometry, i.e. without the parallel postulate). The one major exception to this in practice is the [[axiom of choice]], as the majority of researchers usually do not worry whether a result requires it—unless they are studying this axiom in particular.