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My 6 year old wants to know if infinity is an odd or even number. His 38 year old father is keen to know too.

  • 32
    "Odd" and "even" are typically only applied to natural numbers, of which infinity is not. "1.4" is neither odd nor even as well.2011-07-02
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    Neither or both because $\infty=2\cdot \infty=2\cdot \infty + 1$2011-07-02
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    @The Chaz. Not true. In fact 1.4 = 7/5 is odd when considered as an elt of the subring of rationals expressible with odd denominator. To say that the concept of parity in $\mathbb Z$ doesn't apply to extensions is to miss the point. The question is whether the notion of integer parity can be *extended* in a meaningful way to certain extended "number" systems.2011-07-02
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    @Bill: I didn't have time to type-out the decimal expansion of an irrational! (But seriously, thanks for the comment)2011-07-03
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    @The Chaz. Ditto for irrationals, e.g. $\:\sqrt{3}\:$ is odd in $\:\mathbb Z[\sqrt{3}]\:.$ See [here](http://math.stackexchange.com/questions/26837/do-odd-imaginary-numbers-exist/26843#26843) for more.2011-07-03
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    I would answer yes. ;)2011-07-03
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    Alas! $$$$$$$$.2011-07-03
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    Related MathOverflow question: http://mathoverflow.net/questions/69461/on-the-difference-between-two-concepts-of-even-cardinalities-is-there-a-model-of2011-07-04
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    Infinity is not a number to start with :)2015-08-19

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