"Are there more real numbers between 0 and 1 or between 0 and 2?"(adsbygoogle = window.adsbygoogle || []).push({});

If you ask this question to a present day mathematician, he/she would answer that they have the same amount of numbers. Why? Because for every x in the set of numbers between 0 and 2 (call this set A), there is a corresponding number x/2 in the set of numbers between 0 and 1 (call this set B). Thus both set A and B have the same number of elements.

But this type of reasoning seems very subjective to me. If instead of mapping from x -> x/2, you map from x -> x/3, then you conclude that there are more elements in set B! Furthermore, if you map from x -> x, then you conclude that set A is bigger! Thus, by changing your mapping you can just about say any thing: |A| > |B|, |A| < |B|, or |A| = |B| !

I don't get it. I thought math is suppose to be objective, not subjective?

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

Dismiss Notice

Join Physics Forums Today!

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

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

# Countability: Subjective or Objective?

Loading...

Similar Threads - Countability Subjective Objective | Date |
---|---|

I Countability of ℚ | Feb 12, 2018 |

B Probabilities associated with temporal uncertainty | Jun 27, 2017 |

B Probability Distributions (Countably Infinite domain) | Feb 25, 2017 |

I If Ramsey cardinals exist, all powers using Def are countable? | Jun 8, 2016 |

Is Baire Space countable? | May 21, 2014 |

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