In some countries, it is illegal to destroy currency. Currency is only paper, and if I destroy some currency, then the government can print an equivalent amount. I have never been able to understand the logic of this prohibition.
The 50 dollar/pound/euro note that you have in your wallet does not really belong to you: it is the property of the government. Thus destroying it is destroying the property of the government and as said before it will cost money to print new notes. The currency also has a symbolic value of freedom and liberty: the government is sovereign enough to have a currency of their own.
Mikko H T Ovaskainen Dear Mr. Ovaskainen, are you really saying that the $50 dollar note in my wallet does not belong to me? I agree that destroying the note means that I am destroying a piece of paper, but the cost of that small piece of paper CANNOT be more than $50.
I am not an expert in this so just my thoughts: the note itself does not have a value, the value is held by the government in gold reserve or in whatever that makes the 50 dollar note worth 50 dollars. It's more like an IOU: you have the control of the note but do not own it. And there is little you can do to make the note more valuable, 50 dollars is 50 dollars, like you can with items that you own, like your car or apartment.
Someone from economics would be able to give a more rounded and accurate answer.