[Verse 1]
Picture arrows flying from set A to B
Each one landing where it's meant to be
Injective means no crowding at the target
Different inputs keep their distance, never market
The same output twice, that's the golden rule
One-to-one mapping, mathematician's jewel
[Chorus]
Functions have their personalities
Injective, surjective, bijective qualities
Arrows tell the story, watch them as they fly
One-to-one means spreading out across the sky
Onto means every target gets its share
Bijective is the perfect love affair
[Verse 2]
Surjective paints a different kind of scene
Every element in B must be seen
At least one arrow finds each destination
No lonely points in this equation
Onto function covers all the ground
Every output value must be found
[Chorus]
Functions have their personalities
Injective, surjective, bijective qualities
Arrows tell the story, watch them as they fly
One-to-one means spreading out across the sky
Onto means every target gets its share
Bijective is the perfect love affair
[Bridge]
When injection meets surjection
That's bijection's sweet connection
Perfect pairing, nothing missed
Every element gets kissed
Exactly once, no more, no less
Mathematical tenderness
[Verse 3]
Test injection with this clever phrase
If outputs match, inputs must be the same always
For surjection, scan the codomain
No element should cry alone in vain
Bijection builds the strongest bridge
A flawless mathematical privilege
[Chorus]
Functions have their personalities
Injective, surjective, bijective qualities
Arrows tell the story, watch them as they fly
One-to-one means spreading out across the sky
Onto means every target gets its share
Bijective is the perfect love affair
[Outro]
From domain to codomain the arrows dance
Giving every function its chance
To show its type with crystal clarity
One-to-one, onto, or both in harmony