Re: Relative Cardinality

mueckenh@xxxxxxxxxxxxxxxxx wrote:
> > Er ... Euclid proved that there are an _infinite_ number of primes.
>
> Euclid did not talk of infinity. There are more than any given number,
> he said.

That's what people call "infinite." Let's take apart the word, first
it starts with IN, which means that the latter part of the word is
negated, now the other part of the word is FINITE. Now FINITE means
"less then some natural number n". Since there is no natural number n
such that the number of primes is less then that particular n, then one
concludes that the number of primes is NOT FINITE. Another way to say
that there are INFINITELY many primes.

So of course Euclid did not talk about "infinity," because he wasn't
speaking english and had used greek. I'm not sure what greek for "not
finite" is, but english is "infinite."

Jiri

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