From numbers like googol, bigger than the number of atoms in the universe, to infinities that come in different sizes despite all being infinite — math stretches far beyond what our intuition can reach. Let's go a little further this time (some of this content is high-school level).
Korean and English name numbers differently depending on how many times 10 is multiplied. Move the slider through powers of 10 and check the unit names.
Intuitively, it feels like "infinity is just infinity, all the same size" — but the 19th-century mathematician Georg Cantor proved that infinity comes in different sizes too.
Suppose you could list every real number between 0 and 1 in order. Change just one digit at each diagonal position, and you can always build a new number that isn't anywhere on the list — which means such a list was never possible to begin with.