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Infinity is not a number. If you want to extend even/odd to it, you can pick whatever you want.



There's always someone who sees a question in a submission title and feels the need to comment simply to answer said question in the most boring, banal, and least insightful way possible. Most people realize that if an article that poses a seemingly-simple question makes it to HN frontpage, there's almost certainly some unexpected, interesting, and/or insightful discussion there that reveals that the question wasn't so simple after all.

Almost everything interesting in mathematics stems from a simple question: "How could we extend a concept to be more generally applicable?" Saying that infinity is not even or odd because it's not a number is like claiming that matrices can't be multiplied because they are not numbers.


I am not preventing the discussion or claiming that you shouldn't extend this concept, just objecting to the way to question is formulated ("is infinity an odd or even number"). The stackexchange comments agree with me, and do this extension by pointing out reasons it would be useful to pick one or the other, but I found it important to point out this caveat that there is no logical answer (in terms of numbers) and whatever you pick would be an extension, not a conclusion.

Nowhere in my comment do I say that this is a silly submission or suggest that it shouldn't be in the front page.


Ordinals are often also called ordinal numbers. Both ordinal and cardinal numbers are very much generalisation of natural numbers to a more general concept of number, depending on if you see counting sizes of sets or denoting position (e.g. first, second, etc.) as the fundamental thing numbers do. Of course there are also other notions of number that focus on other aspects (e.g. number fields). But I think it's definitely not wrong to call all of these things numbers.

So it seems weird to me to object to the form of the question, it is perfectly fine as it is. If the question was "is infinity an odd or even natural number?", then of course you'd be right.

All of these things are also stuff one could discuss with a 6 year old (i.e. tell them that there are multiple notions of numbers that focus on different aspects, and that the question has a different (probably interesting) answer in each of these different contexts). Insisting that infinity is not a number seems like a less interesting way to talk about this, without even being necessarily more rigorous.

Edit: See also [0], linked in the second answer

[0]: https://math.stackexchange.com/a/36298


I suggest you reread the OP and ask questions, because you seem to have overlooked some of the ideas explained therein, such as transfinite ordinals.


You can build those and then pick if you want them even or odd, which are regular-number concepts. That is exactly what they did, and what I described. You go and re-read it.




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