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by gowld
2246 days ago
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In math, when assuming the existence of something proved a contradiction, we conclude that the thing does not exist. The description may exist "integer between 3 and 4", but there is not described object. A description names a set or a class, and that class can have 0,1, or more numbers. |
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Well only to the extent that you don't want to throw away any of the other axioms. Sometimes you do and there are some fun systems of math, but few have any practicality and those that do are often so advanced that even someone with an undergraduate focus in math can't appreciate those systems.
It is much the same with computer science. I personally enjoyed playing around with formal concepts of computation and adding some extras to see what happens. For example, what happens to a Turing machine if part of the machine can time travel or has access to an oracle. Does this make concepts like time travel inherently contradictory to our notion of computation?
But the practicality of these exercises does not exceed their entertainment value.