Most Math Problems Do Not Have a Unique Right Answer • Hacker News Board

Post by j2kun » Mon, Aug 04, 2014, 10:55 PM UTC

JadeNB wrote: post #70

j2kun wrote: post #66

Earlier quoted context omitted.

The question is, "What do you define as a 'problem'?" You need to answer that before you can make claims like "we can all agree..." and give an example of something that I don't agree is a problem (if you're saying what I think you're saying).

My weak, but (I think) practical, implicit definition of 'problem' was: > a question that a mathematician might ask I agree that this is not a very useful definition, by virtue of its extreme and probably excessive inclusiveness, but I think that it's hard to do any better without using words like 'interesting' that themselves need careful definition. (It's fair to argue that my definition in turn requires clarificat…

You're falling into the interesting number paradox here, regardless of not using the word interesting. You can't make a statement about the cardinality of a set if your definition of that set isn't expressed using mathematics. In other words, you're saying "I'm not going to give a mathematical definition of this thing, but I can nevertheless give a mathematical proof of a mathematical statement about that thing."

For example, why is the set of all questions utterable by humans not a countable set? By that reasoning there are more numbers than questions!