# Difference between countable and uncountable infinity

**URL:** https://boards.straightdope.com/t/difference-between-countable-and-uncountable-infinity/330430
**Category:** Factual Questions
**Created:** [November 10, 2005, 5:19pm UTC](https://boards.straightdope.com/t/difference-between-countable-and-uncountable-infinity/330430 "2005-11-10T17:19:52Z")
**Posts on this page:** 1
**Page:** 2

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### Author: ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)
#### Post date: [November 14, 2005, 4:58am UTC](https://boards.straightdope.com/t/difference-between-countable-and-uncountable-infinity/330430/21 "2005-11-14T04:58:05Z")

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> [@ultrafilter](#):
>
> Only if you don’t believe the axiom of choice.

Well of _course_ one must believe in the axiom of choice. It’s the well-ordering principle that’s plainly false.

And Zorn’s lemma… who knows?

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