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.
Is infinity an odd or even number?
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infinity
parity
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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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19Neither or both because $\infty=2\cdot \infty=2\cdot \infty + 1$ – 2011-07-02
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17@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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0@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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4@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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1I would answer yes. ;) – 2011-07-03
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0Alas! $$$$$$$$. – 2011-07-03
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0Related MathOverflow question: http://mathoverflow.net/questions/69461/on-the-difference-between-two-concepts-of-even-cardinalities-is-there-a-model-of – 2011-07-04
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4Infinity is not a number to start with :) – 2015-08-19