Just suppose ...
In an infinite universe, which has existed for infinite time,
suppose 6.4 x 10^28 protons, neutrons and electrons, randomly assembled to form an intelligent being, (again), which then invented radio detection. This being then looked for exo-planets, and found one which may reside in a liquid water capable Habitable Zone (LWCHZ), 600 Lyrs distant.
This means that out of approx 3^10^28 possible randomly assembled configurations of sub-atomic particles, at least one instance of radio capable, sub-atomic combinations, is presently known to exist per LWCHZ.
A project called “SETI” looks at the exo-planet with a deep space radio network. They receive no recognisable signals. They conclude a ‘low probability’ that intelligent exo-life exists on that planet .. their search goes on.
How far does mathematical theory say they have to go to find a radio-capable ET being, based on this new evidence ?
3^10^28 x 600 Lyrs = 3^10^28 x 600 x (9.46073 x 10^12) kms
which is approx = (3^10^28) x 10^14 kms.
Anything beyond 62 x 10^9 Lyrs (approx 587 x 10^21 kms), comoving, is beyond causal contact for this radio capable assemblage of sub atomic particles, which live in a LWCHZ. So, based on this new evidence, it seems this particular hypothetical instance of SETI, would never receive intelligent ET radio signals, according to the mathematical concept of ‘The Infinite Universe’, and the known Laws of Physics.
Cheers