Tag: Cardinality of the continuum

Not a proof that aleph null and the order of the continuum are the same
One final point from Wheels, Life and Other Mathematical Amusements– this time a “nonproof”. Some argue that the order of the counting numbers, is the same as that of the continuum – in other words that there is no difference in the scale of these two infinities. Here is an argument that is sometimes advanced…

Cardinality of strings … 2
I have to make a confession. When I wrote the post below I was genuinely puzzled by the issue and what seemed to be a mistake in P, NP, and NPCompleteness, but just as I was about to press “publish” I saw that several pages earlier Professor Goldreich had stated: “We consider finite objects, each…

Cardinality of the set of all strings
I finished John Naughton‘s A Brief History of the Future: Origins of the Internet – an interesting diversion, to be sure and a book worth reading (not only because it reminds you of how rapidly internet adoption has accelerated in the last decade.) By now I should be on to proper revision, but I indulged…