This is about the ordinal numbers, which (except for the finite ones) are less well known than the real numbers, although theoretically simpler.
The numbers of either kind compose a linear order: they can be arranged in a line, from less to greater. The orders have similarities and differences:

Of real numbers,

there is no greatest,

there is no least,

there is a countable dense set (namely the rational numbers),

every nonempty set with an upper bound has a least upper bound.


Of ordinal numbers,

there is no greatest,

every nonempty set has a least element,

those less than a given one compose a set,
 every set has a least upper bound.

One can conclude in particular that the ordinals as a whole do not compose a set; they are a proper class. This is the BuraliForti Paradox.