[Verse 1]
Let's start with sets, collections we can see
Elements inside, like numbers one two three
Relations connect them, pairs that correspond
Functions map each input to one beyond
Proofs build our foundation, logic we can trust
Mathematical thinking is absolutely must
[Chorus]
Sets and strings and functions too
Sigma star will see us through
Empty epsilon, concat flow
Mathematical base we need to know
Power sets and products cross
Without these tools we'd be lost
[Verse 2]
Alphabets aren't letters in a book
They're symbols sigma, take a closer look
Strings are sequences, characters in line
Languages are sets of strings designed
From finite to infinite they grow
Building blocks of what we need to know
[Chorus]
Sets and strings and functions too
Sigma star will see us through
Empty epsilon, concat flow
Mathematical base we need to know
Power sets and products cross
Without these tools we'd be lost
[Bridge]
Kleene star means zero or more
Concatenation joins what came before
Empty string epsilon stands alone
Power sets make subsets known
Cartesian products pairs combine
Every element with every line
[Verse 3]
Relations can be one to one or many
Functions must be single, not just any
Proof by contradiction, assume it's false
Direct proof follows logical pulse
Induction starts with base case strong
Then proves the pattern carries on
[Chorus]
Sets and strings and functions too
Sigma star will see us through
Empty epsilon, concat flow
Mathematical base we need to know
Power sets and products cross
Without these tools we'd be lost
[Outro]
Now we have our foundation laid
Mathematical tools we've made
Ready for automata's call
These preliminaries guide us all