[Verse 1]
Take any set you know by heart
Count every element inside
Now build its power set apart
Each subset waits to be your guide
The members multiply like stars
No mapping scheme will ever reach
From old to new, the distance far
Cantor's wisdom starts to teach
[Chorus]
Size of S is always smaller
Than its power set's domain
P of S grows ever taller
No surjection can contain
Diagonal proof cuts through the maze
Shows the gap that never fades
Infinity has endless ways
To build new mathematical trades
[Verse 2]
Start with naturals, aleph-null
First infinity we meet
But P of N breaks every rule
Makes continuum complete
Two to the aleph-null we find
Then power set again we take
Each level leaves the last behind
New cardinals in our wake
[Chorus]
Size of S is always smaller
Than its power set's domain
P of S grows ever taller
No surjection can contain
Diagonal proof cuts through the maze
Shows the gap that never fades
Infinity has endless ways
To build new mathematical trades
[Bridge]
No largest cardinal exists today
The tower climbs without an end
P of P of P all the way
Each floor transcends what we extend
Suppose a function onto tries
The diagonal will prove it wrong
Self-reference cuts the ties
To any mapping scheme too strong
[Chorus]
Size of S is always smaller
Than its power set's domain
P of S grows ever taller
No surjection can contain
Diagonal proof cuts through the maze
Shows the gap that never fades
Infinity has endless ways
To build new mathematical trades
[Outro]
Cantor showed us truth profound
No set maps onto its power crown
In the realm where logic's sound
Hierarchies spiral up, not down