[Verse 1]
When you need to prove infinity's claim
Start with one domino in the chain
Base case first, check it's true
Then assume what P of k can do
[Chorus]
Base and step, that's the trick
Mathematical induction's quick
Prove it works for number one
Then show k leads to k plus one
Dominoes will tumble down
Infinite truth is what we've found
[Verse 2]
Take the sum from one to n
Equals n times n plus one, then divide by two
First check one equals one, it's right
Now assume our formula's tight
[Chorus]
Base and step, that's the trick
Mathematical induction's quick
Prove it works for number one
Then show k leads to k plus one
Dominoes will tumble down
Infinite truth is what we've found
[Bridge]
Add k plus one to both sides clean
Factor out what can be seen
K plus one times k plus two over two
The pattern holds, the proof pulls through
[Verse 3]
Strong induction takes them all
Every case before the call
Well-ordering finds the least
Contradiction ends the feast
[Chorus]
Base and step, that's the trick
Mathematical induction's quick
Prove it works for number one
Then show k leads to k plus one
Dominoes will tumble down
Infinite truth is what we've found
[Outro]
Finite minds prove endless claims
Through induction's clever games
Set the chain and flick the start
Mathematics' beating heart