How Many Numbers There Are Between 0 and 1?

There is no number 'next to 0'. In the Reals if \(a>b\) then there exists c such that \(a>c>b\) (let \(c = \frac{1}{2}(a+b)\) for example). The cardinality of any non-zero length interval in R is Aleph One, the same cardinality as all of the Reals as a whole. This is strictly larger than the number of whole numbers, which has cardinality Aleph Null. There's many different types of infinity, these two being the most basic and familiar (but no necessarily the two smallest, due to the Continuum Hypothesis).

Anyway, this is a very old thread so I'm going to close it. If someone wants to talk about the subject anew then start a new thread.

 

Log in or Sign up to hide all adverts.