Since i joined bitcointalk forum i find it difficult to make a post relating to bitcoin, bitcoin is like physical money (fiat), and i want to know the difference between fiat and bitcoin, and without fiat existence can bitcoin have a name?, after thinking all this with seriousness i concluded that bitcoin and fiat works like brothers and sisters and no one can leave each other, so i want to know if any other digital currency can function without fiat?.
Long story short :
Yes it can exist without fiat but not right now.
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It's a seperate entity and you might live in a country where bitcoins are used very often and you are able to pay with it in every corner but in most countries, it's not the option, bitcoins is used but the only way you can use it is by exchanging or trading online or offline.
Therefore at some places it certainly can but most of the times you would find it hard to live just on bitcoins but have you heard of the family travelling the world just by using bitcoins???
Google it!
( They might believe otherwise, quite an interesting read!)