# Cardinality of Infinite Sequences of Integers

I am having trouble answering a question about the cardinality of the infinite sequences of integers.

I claimed that the cardinality would be $\aleph_0^{\aleph_0}$, which would be $2^{\aleph_0} = \mathfrak c$.

According to my instructor, I have the right answer, but am lacking idea/intuition.

My ideas start as that:

An infinite sequence of integers will be denumerable and because of that, the cardinality of a particular infinite sequence will be $\aleph_0$.

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So, what are you asking? – Cameron Buie Nov 14 '12 at 21:08

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I think that almost all the questions I saw by you were already answered on the site at least once (and probably more). Have you tried using the search feature? – Asaf Karagila Nov 14 '12 at 21:09

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Exactly what did you say to justify the conclusion that there are $\aleph_0^{\aleph_0}$ infinite sequences of integers? We can’t even guess what your instructor thought was wrong if we don’t know what you said. Was it what you wrote in the last paragraph of the question? – Brian M. Scott Nov 14 '12 at 21:12

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@JulianPark: I had none, either, when I started here. There are many tutorials on the web. You can also right-click any $\LaTeX$, Show Math As -> TeX commands and see how it was done. – Ross Millikan Nov 14 '12 at 21:27

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– Asaf Karagila Nov 14 '12 at 21:38
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