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When there will not be any new fouls to "invest" in Bitcoin, the system will collapse.
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Bitcoin will not collapse if nobody "invests". It does not need investors. It works well regardless of the value of a bitcoin.
what you mean with "works well" ?
if nobody investing(come with new money in system), who will use it then?

please explain. let's say you want to "sell" your bitcoin. to whom will you do it?
You can sell it to those that already accept bitcoin
Do you not see the difference between a ponzi scheme and bitcoin that works eventhough there is no incoming money?
Its better if more join in but it still WORKS without new people having to constantly buy more. ponzy schemes dont work at all if there is no incoming money.
then Bitcoin should not be related to fiat currency at all.
Imagine that you have an online store who is selling laptops and you accept bitcoin.
you already "bought" these laptops from a manufacturer with 1000 usd each and you want to sell with 1500 each.
You see that the bitcoin price is 1BTC = 270 USD and you set 5 BTC for one laptop.
someone is buying one laptop with 5 BTC BUT you as a business(company) needs to pay your bills(gas, salaries, electricity) too and nobody is accepting Bitcoin. You will want to get cash for your 5 BTC.
You will have to find an exchanger and when you want to exchange...surprise !.
5 BTC = 900 USD because the Bitcoin price fell.

you have loss even you did your work very good.
Bitcoin is a speculative bubble that is, a special kind of fad, a mania for holding an asset in expectation of its appreciation.