We claim that a set $A$ is finite if and only if there exists some $kinmathbb N$ these types of that there exists $filecolon Ato ninmathbb Nmid nCookie Settings
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Does there exist an infinite discipline with characteristic $p$ for just about any prime $p$ that is not way too large? ninety six
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YuryYury seven,0952424 silver badges2727 bronze badges $endgroup$ three $begingroup$ This instance ignores the loading of absolute-summability during the def'n of expected price of a random variable getting countably infinite values. With no this kind of loading, "expected price of a random variable using countably infinite values" does not have plausible meaing on account of Riemann Rearrangement Thm, and irresistant to vary with the phrases in the sequence itself.
For instance, the list of all pure figures $mathbb N$ is "infinite" in cardinality, in actual fact "countably infinite" -- but its cardinal $aleph_0$ and the ordinal $omega$ Infinite Craft which is the "get type" of $mathbb N$ are described as being "transfinite".
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