Consider two identical sets, A and B; but they're not identical, because they have different names. Paradox?

Say I have a sequence of numbers - 1,2,3,4,5,6,7. I add 1 to 7 to create the next number in the sequence,8. The sequence is finite. I add 1 to 8 to get the next number in the sequence, 9. The sequence is finite. I keep on going... At what point does my sequence become infinite? How can my sequence ever become infinite?

Any two sets have different conditions for membership, so if object O is in set S because it's blue or green, then being blue or green cannot be the reason why any other object is in any other set. If so, how can there exist a set of green objects?

Two different sets cannot have the same reason for membership, so if beauty is the reason why a painting is in the set of beautiful paintings, then beauty cannot be the reason why the painting is in any other set, such as the set of good paintings. Is that fair?

Fred is 14. Would you agree that Fred isn't in the set of people aged less than 15 because he's 14, he's in the set of people aged less than 15 because he's less than 15? (It doesn't matter what his age is, as long as he's less than 15.)

My Mom told me that "there's always somebody better than you!". I was thinking if that was true or not because there are not an infinite number of people in the world, so at some point you will reach somebody who is the best, right? For example, if person A was the best person at art in the world, there wouldn't be anybody else who can possibly be better at art than them.

No two sets can have the same conditions for membership, so if Miss X is in the set of young girls because she's a young girl, then she cannot be in the set of female humans because she's a young girl. Paradox?

Lots of science today (meteorology, cosmology) is based on computer simulation or modeling for those phenomena that are difficult to observe directly. If a computer simulation gives me a result consistent with what we can see (star distribution for two galaxies that collide) can we infer that the underlying process is the same in the simulation and in physical world? The simulation is just numbers (or symbols) input as data about the system(s) modeled. Are numbers the underlying "stuff" of objects, too, rather than atomic particles, etc.?

If I investigate the Goldbach conjecture by testing individual even integers to verify that they accord with it, do I have more reason to believe that the conjecture is true the more integers I verify? Or am I in just the same epistemic position regarding the conjecture whether I've verified one integer or a billion?

In mathematics, it is commonly accepted that it is impossible to divide any number by zero. But I don't see why this necessarily has to be the case. For example, it used to be thought of impossible to take the square root of a negative number, until imaginary numbers were invented. If one could create another set of numbers to account for the square root of negatives, then what is stopping anyone from creating another set of numbers to account for division by zero.