Resolution: All whole numbers are interesting.

It has been a lot of fun for me, as I've had to do quite a bit of research to understand how exactly a number can be classified as "interesting. " And learning about expository numbers has also been quite fun. On with my final statements! ". .. all numbers and math terms have verbal representations in the English language. .. " I'm obviously not disputing this statement, but your claim that because there is a finite amount of English words, there is a finite number of ways to describe the uniqueness of a number that differentiates it from all other numbers is fallacious. That's like saying there's a finite amount of whole numbers because after a certain point, we will run out of names for them (or it will be so large we won't have enough time in our lives to say the number). Just because it would take an arbitrarily-long amount of time to describe the uniqueness of a particularly large number doesn't prove that limits the uniqueness of the number itself. The fact you can represent the interesting qualities of a number numerically demonstrates this. Claim disputed. ". .. my opponent hasn't shown why each individual prime number is interesting. .. " I was simply making a point that there are many ways to classify numbers, each of which can be considered interesting. Obviously your idea that numbers have to have a unique property to be considered interesting would discredit the idea that prime numbers are interesting because they are prime, which I used to my advantage in my expository numbers proof. However, my expository number proof would, then, show that large prime numbers are interesting (not because they are prime, but because they have a unique and interesting representation in expository form). Point defended. "However, . http://www.cadaeic.net......... actually shows something different; the study was actually only completed for all whole numbers below 1000. " I encourage Con to go back and read the article again: "These results suggest that every integer > 999 is an expository number in hundreds of thousands of ways, or more. Surely it will be possible to find one or two of these whose intersection of solutions sets is just the value n. Note that we have deliberately limited ourselves to the intersection of two sets. We could take three or more, if necessary, in order to obtain a property that n uniquely satisfies, but we conjecture that this will never be needed. [1]" They stopped at 1,000 because it was unnecessary to continue. Every number in the range of 900-999 has over 145,000 different variations of being an expository number, and with enough time and research, there would be enough intersections between those variations that would give each number a unique expository property. Refer back to my 135 example in Round 2. The proof suggests very, VERY strongly that every number above 1,000 is uniquely expository. Point defended. "We are debating whether all primes numbers are interesting, not whether there are no uninteresting numbers. .. my opponent's claim reached a paradox - two of the results found contradict each other. Therefore, no conclusion can ever be made from that claim. " First, my proof by contradiction was not just talking about primes, but all whole numbers. Second, the fact there's a contradiction means the original proposition in the proof is untrue. Namely, that there are no uninteresting numbers. I feel there may have been a miscommunication there. Point defended. "I challenge my opponent to find what is interesting about [the number 76941309571390671361571395]. " This is an argumentum ad ignorantiam [2], and thus is irrelevant. Let's recap: My proof by contradiction that shows all whole numbers are interesting was attacked and properly defended. My opponent's claim that English has a finite number of words is irrelevant in determining whether all whole numbers are interesting or not. My demonstration that all numbers above 119 are expository and uniquely so (thus meeting Con's requirements of a number being "interesting") remained uncontested. With all of this information to consider, it should be clear what the decision in this debate is. Vote Pro. Again, a final thank you to Con, and I look forward to hearing his final defense and closing statements. Sources: [1] . http://www.cadaeic.net... [2] . http://philosophy.lander.edu...