Is ∞ odd or even?

Is ∞ odd or even?

This question popped into my head yesterday, and had already been asked and answered nicely on math.stackexchange.  I liked Qiaochu Yuan's answer the best...

math.stackexchange.com/a/49045/300001

...as well as the related question/answer he linked to, "Is infinity a number?"

math.stackexchange.com/questions/36289/is-infinity-a-number

Great reading.  I find questions like this so interesting because they take some concept in one context and try to meaningfully extend it to another context.
http://math.stackexchange.com/questions/49034/is-infinity-an-odd-or-even-number#

Comments

  1. Refurio AnachroFebruary 6, 2016 at 12:08 PM

    I'm surprised to learn that there's a nice, meaningful and intuitive answer to that question! Thanks Roice Nelson​!

    ReplyDelete
  2. Richard GreenFebruary 6, 2016 at 9:32 PM

    I agree this is a great answer for cardinal numbers, but one of the other answers for ordinal numbers is also very good (and reaches a different conclusion).

    ReplyDelete
  3. Refurio AnachroFebruary 7, 2016 at 4:23 AM

    I did anticipate much of Qiaochu Yuan​​​'s answer, but now that you've made me actually read it, Richard Green​​​, I'm glad I did! Thanks to both of you.

    The other question, "is oo even?" caused my intuition to rattle like "what's arg(0)?!" so I had to look. JDH's answer quickly silenced my confusion, and boy - that felt good! Supersonic insight pleasure.

    ReplyDelete

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