[Verse 1]
Count every number that you know by name
One, two, three, four - seems like a simple game
But take those numbers, make a bigger collection
Every subset hiding in their reflection
Two to the power of however many you start
That's the magic tearing infinity apart
[Chorus]
Never-ending staircase, climbing floor by floor
Every time you reach the top, there's always something more
Power sets keep growing, doubling what you had
Cantor showed us truth that drives mathematicians mad
No ceiling, no limit, just stairs that multiply
The staircase builds itself into an endless sky
[Verse 2]
Start with just three elements, call them A, B, C
Their power set contains eight possibilities
Empty set, each single piece, then pairs combined
Plus the set of all three - infinity redefined
Each level births the next one, twice as vast and wide
No matter where you stand, there's more on the other side
[Chorus]
Never-ending staircase, climbing floor by floor
Every time you reach the top, there's always something more
Power sets keep growing, doubling what you had
Cantor showed us truth that drives mathematicians mad
No ceiling, no limit, just stairs that multiply
The staircase builds itself into an endless sky
[Bridge]
Even infinite sets bow to this cosmic law
Their power sets stretch beyond what minds can draw
Aleph-null meets aleph-one in this parade
Each infinity spawning larger infinities made
The theorem whispers: "Think you've found the end?
Watch me build another floor around the bend"
[Chorus]
Never-ending staircase, climbing floor by floor
Every time you reach the top, there's always something more
Power sets keep growing, doubling what you had
Cantor showed us truth that drives mathematicians mad
No ceiling, no limit, just stairs that multiply
The staircase builds itself into an endless sky
[Outro]
So when you think you've counted everything that is
Remember Cantor's gift, this mathematical quiz
The power set's always larger than the set you knew
Forever building upward, making one from two