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You may like the whole list of constructive gems and stones then: http://math.andrej.com/category/gems-and-stones/ http://math.andrej.com/category/gems-and-ston
by edflsafoiewq 7y ago
You may like the whole list of constructive gems and stones then: http://math.andrej.com/category/gems-and-stones/ http://math.andrej.com/category/gems-and-stones/ :)
As a sampler, the following are all constructively false (ie. imply the law of excluded middle)
* Every finite set can be enumerated without repetitions
* A subset of a finite set is finite
* The intersection of finite sets is finite
- lonelappde 7y agoNote that these results rely on a technical definition of set that is rather abstract mathematically, in a way programers may find amusing. It defines a set as a potentially infinite list with potential duplicates, from which we can observe that some lists cannot be deduplicated in finite time, making certain operations that are easy on computer science sets not always possible on computer science lists. For example, is A a subset of B={0}, if all you know about A is that it is a Java iteratable that returns 0 for the first 10^3000 elements you examine?