Lets say I have [itex] \aleph_1 [/itex] numbers of sets that each have [itex] \aleph_1 [/itex](adsbygoogle = window.adsbygoogle || []).push({});

number of elements and I want to show that the union of all of these sets has

[itex] \aleph_1 [/itex] number of elements.

I start with the line segment [0,1] and shift this line segment up by all the reals from 0 to 1.

So now we have the unit square. Now we want to show that this unit square can be mapped to [0,1]. So can we use trick where you take the decimal form of a point and expand it to 2 dimensions. [itex] (.x_1x_2x_3x_4......)\rightarrow (.x_1x_3...),(x_2x_4....) [/itex]

or another thought I had was to take the cantor set and move it around with a set of reals and map each set to a cantor set that was shifted across the real line.

**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!

# Proof about size of a union of sets.

Loading...

Similar Threads - Proof size union | Date |
---|---|

I An easy proof of Gödel's first incompleteness theorem? | Mar 6, 2018 |

I Standard Deviation Versus Sample Size & T-Distribution | Dec 20, 2017 |

I Cantor's decimal proof that (0,1) is uncountable | Sep 27, 2017 |

A A "Proof Formula" for all maths or formal logic? | Apr 19, 2017 |

I Regarding Cantor's diagonal proof. | Feb 28, 2017 |

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