Congratulations! You just uncovered the premise of Cantor’s diagonal argument , which demonstrates this very thing: that there are an infinite number of infinite sets, each of a different size.

Also for some reason I can’t ever wrap my head around, this idea bothers some religious faith leaders enough to want the teaching of it banned in public schools. ¯⁠\⁠_⁠(⁠ツ⁠)⁠_⁠/⁠¯