3 ms·
Though, if we apply your requirement, the set of problems without a unique answer must be countable as well. So, the cardinality of problems with a unique answ
by dbecker 12y ago
Though, if we apply your requirement, the set of problems without a unique answer must be countable as well. So, the cardinality of problems with a unique answer is still equal to the cardinality of problems without one.
- j2kun 12y agoYou're just using the terminology imprecisely is all. (Indeed, two things being countable does not mean they have the same cardinality; finite sets are also countable)
- dbecker 12y agoI think it's trivially obvious that both sets are infinite. There are infinitely many addition problems involving two numbers, and that's a subset of the set of problems that the article claims to be smaller.
- j2kun 12y agoI'm not making claims about the truth or falsity of your statement, just critiquing the logic and terminology you're using (the lack of a definition for a "problem," the minor misuse of the term "countable"). Regardless, I really hope you saw the article as something besides a mathematical claim, because it clearly did not pretend to be one.
- dbecker 12y agoIndeed. My original comment was meant as a joke, not as a serious mathematical claim.