[Verse 1]
Mathematical statements hide their secrets well
Universal quantifiers cast their spell
"Every function" starts the theorem's dance
"For all" means no exceptions get a chance
When you see those English words unfold
There's formal logic waiting to be told
[Chorus]
Read between the symbols, parse each line
Every theorem's quantified by design
For all, there exists, and if-then too
Mathematical truth is waiting for you
Universal, existential, conditional chains
Precision flows through logical veins
[Verse 2]
"Every continuous function on closed ground
Is bounded" - let's break that statement down
For all f and intervals a to b
If continuous, then bounded it must be
There exists an M that holds them tight
Absolute values stay within its sight
[Chorus]
Read between the symbols, parse each line
Every theorem's quantified by design
For all, there exists, and if-then too
Mathematical truth is waiting for you
Universal, existential, conditional chains
Precision flows through logical veins
[Bridge]
When negation comes to flip the script
Universal turns existential quick
"Not all" becomes "there exists one"
Where the original statement comes undone
Rigorous thinking splits the informal haze
Quantifiers guide us through the maze
[Verse 3]
English hides the structure underneath
Logic symbols show what we believe
Unpack the language, find the core
Hypotheses and conclusions explore
From casual words to formal thought
Precision is the treasure that we've sought
[Chorus]
Read between the symbols, parse each line
Every theorem's quantified by design
For all, there exists, and if-then too
Mathematical truth is waiting for you
Universal, existential, conditional chains
Precision flows through logical veins
[Outro]
Master this skill and you'll understand
How mathematical truth expands
Every statement quantified and clear
Foundation thinking crystallizes here