That is incorrect. Online calculators take into account current difficulty (i.e., other miners).
Looking at an online calculator (
http://www.alloscomp.com/bitcoin/calculator), you would make about 0.05 BTC/day with 1 GH/s. If you mine with a pool, you could expect to see around 0.05 BTC/day deposited into your QT wallet. If you solo mine, then you will only receive coins when you find a block (25 BTC), and you would expect to find a block every 25 / 0.05 = 500 days on average. So it's the same expected BTC, just different amounts of variance.
Ah ok! I wasn't sure if the difficulty rate was proportionate to the # number of miners, and probably more to do with the combined hashing capacity of those miners correct?
Is mining cumulative? Meaning if I wait those 500 days I should see a payout of the 25BTC or does everything start over once a block is solved? Excuse me if this is stated in Satoshi's original paper, I'm still working through it.