Do I then own the answer to the equation?
Just because you exhaust scarce or rivalrous resources to discover something, does not mean the discovery is scare or rivalrous.
How does my use of an idea, exclude you from using it also?
Suppose that you spend a minute of your time figuring out x + 2 = 4.
You discover that x is 2, I come along and see your work and discover that x = 2.
By having this knowledge have I taken anything from you, by having this knowledge do i prevent you from also having it?
If I write down the equation and it's answer on a piece of paper and sell it for one dollar, have I taken anything from you?
If your answer to the latter question is "Yes, you have taken profit from me." , then you are assuming that you have a right to other people's money, and it would logically follow that if that action was theft because I made money that you potentially could have, so would all forms of competition.
P.S. In your opinion, when is a good scarce and when is it not scarce, when does a scarce good become non scarce?
Also, what is your definition of scarcity?
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"The State is a gang of thieves writ large." - Murray Rothbard
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