The uninteresting paradox

When I say uninteresting, I don’t mean that this paradox is uninteresting. It means “relating to the interesting/uninteresting numbers” and this is a paradox that is about uninteresting numbers.

When we say interesting number, they’re numbers with special features. Like 1 is the first positive integer, 2 is the only even prime, 3 is the first odd prime, 4 is the first composite, and so on. But what about uninteresting numbers?

If the list of uninteresting numbers went 7, 13, 35, 57, 89, 103, 205, 784, 1083, 1849, 3456, 8465, 9172, 10928, 40923, 98402, … then obviously 7 is interesting because it’s the first uninteresting number. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. But wait. For 7 to be interesting, it has to be an uninteresting number, which means that 7 is uninteresting. But wait. There’s no number below 7 that’s uninteresting. So 7 is interesting. (And on and on and on and on and on and on and on and on and on and on and on and on…)

Sorry about that, I just wanted to do it. So what it suggests is that, if the list is as above, then 7 can neither be interesting or the opposite (or it could be both, but what?) because to be interesting, it has to be the smallest uninteresting number (which 7 is), but that also implies that 7 is uninteresting, so it’s not one or the other, but either both or none.

Peace out.

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