How th work with enumerable and infinite set

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asked 10 years ago

Anonymous

updated 2 years ago

tmonteil
27483 ●32 ●205 ●519 http://wiki.sagemath.o...

Hello,

I am trying to do following: construct the set B that is the difference between QQ and the set of the prime numbers (note that B is a countable set). Within Sage, I tried the following

X = Set(QQ)
Y = Set(Primes())
B = Set(X.difference(Y))
B.cardinality()

then I press evaluate. I am expecting that the cardinality of B is +Infinity. But Sage does not bring any result.

I tried this also initializing B like

B = InfiniteEnumeratedSets(RR).

Could anybody please give me a hint what I am doing wrong?

Thank you very much and regards.

vbk

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answered 10 years ago

Luca
890 ●6 ●21

You just found a bug in Sage. Sage does not have enough knowledge to know that the set of rationals that are not prime numbers is infinite. If there was no bug, you'd have an error saying something like "Sage cannot compute the cardinality of B".

However, if you type B.cardinality??, you'll notice that what the function does is simply return len(list(self)), i.e. it constructs the list of ALL rationals that are not prime numbers, and returns its length. You get no answer because it's entered an infinite loop.