And yes Cash can be double spent,
If I give you a $10 bill for a soda, and you are holding on to it in your hands,
Then I slap you upside your head and Take the $10 back and keep the soda,
then walk down the street, and buy some candy with that $10 , I just
double-spent that $10,
and the only proof I did so is that knot on your head.
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Nah. You spent it once on some candy, and stole some soda from me.
Or, if you consider the soda transaction to be complete before you take the $10 back, then you are looking at 3 separate transactions...
Transaction 1: $10 transferred to me from you (in exchange for a soda)
Transaction 2: $10 transferred to you from me (in exchange for a bump on the head)
Transaction 3: $10 transferred to a vendor down the street (in exchange for some candy)
Either way, it's physically impossible to create an equally valid identical copy of that $10 bill (which is the specific "double spend" problem that digital goods need to deal with). That $10 bill can only exist in a single place at any moment in time. The blockchain makes sure that the same is true of digital goods.
This is the only issue that the blockchain solves. It doesn't prevent theft, it doesn't prevent fraud, it doesn't make people intrinsically good (or bad), it doesn't prevent or cause inflation, it doesn't determine exchange rates, etc. It just makes sure that at any moment in time, a given unit of value can only be under the control of a single individual.
Inherently true of ALL blockchain solutions, including both POW and POS, is the fact that there is some period of time between when a transaction is initiated and when the recipient of that transaction can be comfortable with the level of risk which remains that control over that value might change without their authorization.