I'm fairly certain the following is a vector space isomorphism [tex]\phi :\mathbb{R}^\infty\rightarrow\mathbb{R}^\infty[/tex] where the vector space is the space of infinite sequences of real numbers and phi is defined by [tex] \phi(a_1,a_2,...)=(0,a_1,a_2,...) [/tex]. The mapping is linear and the inverse seems to be well defined. Is my logic flawed?(adsbygoogle = window.adsbygoogle || []).push({});

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Isomorphism between R^inf and a proper subset of R^inf

Loading...

Similar Threads for Isomorphism between R^inf | Date |
---|---|

I Isomorphism between 2Z and 3Z | May 2, 2017 |

A Isomorphism between a linear space and its dual | Mar 27, 2016 |

Isomorphism between Clifford algebras CL(4,2) and CL(2,4) | Nov 24, 2014 |

Isomorphism between groups and their Lie Algebra | Mar 19, 2013 |

Question on isomorphism between addition and multiplication | Nov 27, 2012 |

**Physics Forums - The Fusion of Science and Community**