# Imponderable questions

**URL:** <https://boards.straightdope.com/t/imponderable-questions/666094>\
**Category:** Miscellaneous and Personal Stuff I Must Share\
**Created:** [August 13, 2013, 1:02am UTC](https://boards.straightdope.com/t/imponderable-questions/666094 "2013-08-13T01:02:31Z")\
**Posts on this page:** 5\
**Page:** 3

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**Author:** ![chrisk](https://avatars.discourse-cdn.com/v4/letter/c/6de8d8/32.png) [@chrisk](https://boards.straightdope.com/u/chrisk)\
**Post date:** [August 15, 2013, 5:34pm UTC](https://boards.straightdope.com/t/imponderable-questions/666094/41 "2013-08-15T17:34:41Z")

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> [@Little\_Nemo](#):
>
> An infinite number of angels would have an infinite number of eyes, yes?
> 
> All quantities are equal to themselves. That’s axiomatic.
> 
> Therefore, infinity equals infinity.
> 
> That means the number of angels is equal to the number of eyes.
> 
> Conclusion: Angels only have one eye apiece.

Hmm… Most of this actually checks out. I think the flaw is that you’re implicitly dividing your infinite number by itself to get ‘number of eyes per angel.’ Unfortunately, the mathematical rule ‘any number divided by itself equals 1’ breaks down for infinite numbers.

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**Author:** ![BrainGlutton](https://avatars.discourse-cdn.com/v4/letter/b/82dd89/32.png) [@BrainGlutton](https://boards.straightdope.com/u/BrainGlutton)\
**Post date:** [August 15, 2013, 6:43pm UTC](https://boards.straightdope.com/t/imponderable-questions/666094/42 "2013-08-15T18:43:51Z")

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Who put the bomp in the bomp-bomp-bomp-bomp-bomb?

Who put the ram in the rama-lama-ding-dong?

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**Author:** ![Leaffan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leaffan/32/299_2.png) [@Leaffan](https://boards.straightdope.com/u/Leaffan)\
**Post date:** [August 15, 2013, 6:59pm UTC](https://boards.straightdope.com/t/imponderable-questions/666094/43 "2013-08-15T18:59:06Z")

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Do you walk to work, or bring a lunch?

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**Author:** ![Sunspace](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sunspace/32/1250_2.png) [@Sunspace](https://boards.straightdope.com/u/Sunspace)\
**Post date:** [August 15, 2013, 8:57pm UTC](https://boards.straightdope.com/t/imponderable-questions/666094/44 "2013-08-15T20:57:39Z")

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> [@Little\_Nemo](#):
>
> An infinite number of angels would have an infinite number of eyes, yes?
> 
> All quantities are equal to themselves. That’s axiomatic.
> 
> Therefore, infinity equals infinity.
> 
> That means the number of angels is equal to the number of eyes.
> 
> Conclusion: Angels only have one eye apiece.

Actually, according to Cantor’s theory of transfinite cardinals, not only are quantities equal to themselves, but infinite quantities are equal to subsets of themselves. Imagine a hotel with an infinite number of floors, numbered 1, 2, 3, 4… ∞. Now, remove all the even-numbered floors, so that the only floors remaining are numbered 1, 3, 5, 7… ∞. Half as many floors remain, right? But there are still an infinite number of floors! Therefore ∞ = ∞/2. Which means that 2∞ = ∞. And, for that matter, 20∞ = ∞.

So the angels could have any number of eyes each, and there would still be the same number of eyes in total.

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**Author:** ![Shoeless](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/shoeless/32/7099_2.png) [@Shoeless](https://boards.straightdope.com/u/Shoeless)\
**Post date:** [August 15, 2013, 10:51pm UTC](https://boards.straightdope.com/t/imponderable-questions/666094/45 "2013-08-15T22:51:36Z")

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> [@Ambivalid](#):
>
> How much wood could a…Ahh nevermind. 😛

How much wind could a windbreaker break if a windbreaker could break wind?

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