Mathematical Arguments
📋 What it is
A mathematical argument is a chain of justified steps that convinces anyone the claim is true.
🗣️ Coach says
An argument isn’t about winning — it’s about convincing a fair, doubtful reader using only steps they must accept. Each “therefore” has to be earned. If a reader can ask “why?” and you can’t answer, there’s a gap.
🧠 Memory hook
Every “therefore” must be earned. A reader should never get to ask an un-answerable “why?”.
😂 Giggle
Why was the "if-then" statement so bossy?
"IF you accept my premise, THEN you MUST accept my conclusion!"
😲 Whoa!
Mathematicians read each other’s proofs looking for gaps on purpose — a proof isn’t accepted until skeptics fail to break it.
✅ Quick check: Your argument says “…therefore x = 5” but skips why the step before it holds. Is the argument complete?
Say your answer out loud first — then reveal.
No — a skipped justification is a gap; the conclusion isn’t supported until that step is filled in.
An argument is only as strong as its weakest justified link.
🧪 Try it! (2 minutes)
Explain to someone WHY 0 is even, giving each step. Have them play skeptic and ask “why?” at every line.