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Q: Ordinal and Cardinal Limits in Set Theory What are the “limits” of “ordinal” and “cardinal” in set theory? For example, in ZFC, any set is either finite or countably infinite. Also, in ZFC, every ordinal has a cardinal limit, but not every cardinal limit is an ordinal. A: An ordinal has no cardinal limit in ZFC. That is, in ZFC there is no ordinal strictly between $\omega$ and $\omega+\omega=2\omega$. For $n\omega=n(2\omega)$ is an ordinal. On the other hand, the continuum function is a cardinal function in ZFC, and the first uncountable ordinal does exist. EDIT: To answer the additional question “Is there some ordinal strictly between $\omega$ and the first uncountable ordinal?” The answer is no, although it would be interesting to see if a set theoretic proof can be given. The outgoing Secretary General of NATO has publicly criticised the organisation’s insistence on an immediate US and EU ‘targeting’ of Syrian chemical weapons. Jens Stoltenberg, speaking at a meeting of the Alliance’s ambassadors in Brussels, said there must be ‘no doubt’ that Bashar al-Assad had used chemical weapons against civilians but also that he has ‘not crossed the red line.’ ‘We have given Russia, the US and the EU the clear information that the use of chemical weapons will be met by a response,’ Stoltenberg said. ‘This was of course not a surprise, the Organization for the Prohibition of Chemical Weapons has been informed that this kind of weapons would be used.’ Stoltenberg also suggested that the gas used in the attacks might not have come from Syria as the substance is not Syrian and the timing of the attack preceded the country’s expected declaration of its own possession of such weapons. However, the ‘red line’ comment is likely to spark some criticism of the Secretary General. Earlier this month, Stoltenberg said NATO had not set ‘red lines’ for action against Syria, but that it would be ‘shameful if the Syrian regime use chemical weapons against its own people.