Open a maths book and you'll see the infinity sign on almost every page. But is there such a thing ? Can there be? My answer is firmly, No. There is (presumably) the 'non-finite', that concerning which all measurement is irrelevant, but this domain is not accessible to rational thought and experiment, only to mysticism. There is no such thing as the 'infinitely large' or the 'infinitely small', because "If there were no limits there would be nothing" (Parmenides). All phenomena are discrete and all actual entities (as opposed to mathematical ones) have an upper and lower size limit. This principle has radical repercussions: it means, for example, that there is a smallest interval of time, the ksana, during which no change can take place, also a smallest measure of length (no name yet). I believe that during this century science will determine the number of ksanas to a second and the number of 'base-spaces' to a metre and infinity will go the way of phlogiston and the philosopher's stone.
Note: For any questions about this particular event,
please ask Robert Mules.