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Assign order topologies (given by basis sets {x<a} and {x>a} ) to ordinals w and w+1 (w=omega= the first transfinite ordinal).
A sequence f:w->M, where M is a topological space, converges if and only if it can be extended to a continuous function
f':w+1->M.
Such an extension is all about "reaching the infinite".
w+1 as a topological space is isomorphic to
{1-1/n} union {1} in Q under the natural topology in Q.
In general you can embed any countable ordinal in Q.
