# inhabited set

A set $A$ is called *inhabited*, if there exists an element $a\in A$. Note that in classical mathematics this is equivalent^{} to $A\ne \mathrm{\varnothing}$ (i.e. $A$ being nonempty), yet in intuitionistic mathematics we actually have to find an element $a\in A$.
For example the set, which contains $1$ if Goldbach’s conjecture is true and $0$ if it is false is certainly nonempty, yet by today’s state of knowledge we cannot say if $A$ is inhabited, since we do not know an element of $A$.

Title | inhabited set |
---|---|

Canonical name | InhabitedSet |

Date of creation | 2013-03-22 14:25:24 |

Last modified on | 2013-03-22 14:25:24 |

Owner | mathwizard (128) |

Last modified by | mathwizard (128) |

Numerical id | 6 |

Author | mathwizard (128) |

Entry type | Definition |

Classification | msc 03F55 |