it is well known that the upper limit of bitcoins is 21 million, which can be calculated mathematically; but from documents i have read, this is because mining a new block is defined to have diminishing returns (1 halving per 210k blocks); is this the sole factor limiting the possible number of coins? is there anything i missed in this crypto system which becomes more and more difficult over time and finally becomes computationally infeasible that is limiting the number of coins?
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No it does not become computationally infeasible, 1 halving per 210.000 blocks leads to a total of 21m due to math.
Bitcoin block reward is 50 for 210.000 blocks then 25 for 210.000 blocks then 12.5 etc. So the total reward is 210.000 * (50 + 25 + 12.5 + ...). Inside the parenthesis is a geometric series which can be rewritten as 50 * (1 + 1/2 + 1/4 + ...).
Now using the formula in the link we have a = 50 and r = 1/2 and the sum of this infinate series is 100. Multiply that by 210.000 and you get 21 million bitcoins total (actually a little less than that because a bitcoin is not infinately dividable).
