[Verse 1]
Picture dominoes lined up in perfect rows
Each one depends on what the neighbor shows
If first one tumbles and each pushes next
Then every piece will fall as physics expects
But mathematics needs a stricter game
Where logic rules and proof backs every claim
So here's induction, elegant and clean
The strongest method that you've ever seen
[Chorus]
Base case, inductive step, watch them cascade
If P of one is true and transfers get made
From k to k-plus-one without a break
Then every natural number's in your wake
The dominoes must fall, they have no choice
When well-ordering gives structure its voice
[Verse 2]
Start with your base, prove P of one holds true
That's your foundation, solid through and through
Then comes the magic of the inductive leap
Assume P of k, but don't fall asleep
Show that P of k implies the next
P of k-plus-one follows from your text
This chain reaction, once you set it free
Conquers infinite territory
[Chorus]
Base case, inductive step, watch them cascade
If P of one is true and transfers get made
From k to k-plus-one without a break
Then every natural number's in your wake
The dominoes must fall, they have no choice
When well-ordering gives structure its voice
[Bridge]
But why does this work? Let's peek behind
The curtain hiding mathematical mind
Suppose induction fails, some statement breaks
Well-ordering says smallest failure wakes
That counterexample can't be number one
Base case proved that battle's already won
Can't be k-plus-one if P of k succeeds
Inductive step fulfills all logical needs
Contradiction strikes! No failure can exist
The dominoes topple, none can resist
[Chorus]
Base case, inductive step, watch them cascade
If P of one is true and transfers get made
From k to k-plus-one without a break
Then every natural number's in your wake
The dominoes must fall, they have no choice
When well-ordering gives structure its voice
[Outro]
Not just a proof but method supreme
Conquering patterns, the mathematician's dream
From one to infinity, the chain extends
Where logic begins, the falling never ends