I’ve always had in my head the question: what is more “infinite”, the infinity of natural numbers or the infinity of integer numbers?

The concept of infinity is both magical and dangerous, it’s confused, we have heard and used this concept since basic education without caution, simply we have used it.

If you ask somebody, everybody will tell you that integer numbers are infinite, that there are infinity numbers, people use the word “infinity” when they are talking about numbers, I wanna go ahead, what’s the meaning of “there are infinity numbers”?

Maybe sometimes everybody have asked himself the question I started this post with, there are more integer numbers than natural numbers?, or clearly, is the set of integer numbers bigger than the set of natural numbers? Maybe the question sounds stupid, it could be true, What a nonsense, numbers are infinite! or natural numbers are a type of integer numbers, obviously there are more integer numbers than naturals!

Continue reading →