For 10 points, identify this value, denoting a number that is uncountably large.
Hilbert's Grand Hotel paradox concerns sets with this property, and can be resolved by adding prime factors for additional "layers" of this property. This value is the surface area of Gabriel's horn and the perimeter of a Koch snowflake. Georg Cantor introduced the (*) "countable" variety of this concept, which is denoted aleph-null. A monkey with this amount of time will almost certainly type the complete works of Shakespeare. The harmonic series one over n approaches this value as n also approaches it. For 10 points, identify this value, denoting a number that is uncountably large.
Hilbert's Grand Hotel paradox concerns sets with this property, and can be resolved by adding prime factors for additional "layers" of this property.
infinity [prompt on “uncountable” or equivalents] &lt;SR Math&gt;