One thing that probably has not been thought of, during the creation of BTC, is that the number of Bitcoins will be slowly reducing to zero.

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statistically that says bitcoin cannot survive.

Nope. Try the math.

Lets assume that 10% of all the remaining bitcoins are lost every year. That's a ridiculous amount. At today's exchange rate that's a permanent loss from circulation of $882 million dollars worth of bitcoins. I think most people would occur that losses will be much less than that. But, for the sake of argument, how long will it take until there is nothing left?

10 years? Nope. After 10 years there will still be 7322247.24210000 BTC remaining.

50 years? Nope. After 50 years there will still be 108229.27935400000 BTC remaining.

150 years? Nope. After 150 years there will still be 2.874721060000 BTC remaining.

500 years? Nope. After 250 years there will still be 7635.6610000000 satoshis remaining.

1000 years? Nope. After 1000 years there will still be 0.00000000000000036705296286175683 yoctoBTC

Keep adding decimal places (and shifting over the decimal point), and you can keep losing a percentage of what's left and still have more than trillions of spendable units.

The real question is, how do you prove that their bitcoins were in fact lost?

If it's a simple case of lost private key, you can't. Why does that matter?

There are cases of outputs scripts that are provably unspendable. In those cases you can count those bitcoins that are permanently unspendable.

Next generation miners will be treasure hunters. They will recover the lost coins.

This is only possible if mathematical weaknesses are discovered in the cryptographic functions that bitcoin currently uses. I suppose that could happen, but there is no way right now to be certain that such a thing will ever happen.

It'd be nice to exactly know how much bitcoin is in circulation right now

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There was an analysis done in July 2014 that found (at that time) there were a total of 2,745.22283996 BTC that were provably permanently lost:

https://bitcointalk.org/index.php?topic=675321.0