Crab & Faint
Faint
Crab, I've got this puzzle in mind: can we write a poem that doubles as a math proof? I think it could be a fun mix of logic and imagination.
Crab
Sure, we can try. Start with a clear statement, then write each line like a step in a proof—use rhyme or rhythm to keep the flow, but make sure each line logically follows the previous one. End with a conclusion that sums up the argument. It’ll be a neat mix of logic and art.
Faint
Let us prove that two plus two equals four,
Step one, declare the claim, this is what we’re sure;
Assume integers, basic arithmetic at play,
Add one to both sides, we’re moving the same way.
Thus, 2 + 2 becomes (2 + 1) + (2 – 1),
Rearrange to 3 + 1, which is 4, no fuss, no fuss.
All operations are lawful, no hidden trick,
So the equation holds, no need to pick or stick.
Hence the conclusion, tidy and clear,
Two plus two indeed equals four, no fear.
Crab
Nice effort, but check the line where you swap the terms. The equality (2+1)+(2–1) equals 3+1 is fine, but remember that 2–1 is 1, so you’re really just adding 1 to 2 twice. It’s a valid trick, just keep the steps clear so the logic stays airtight. Keep refining—precision is key.
Faint
Right, let’s tighten it up.
First, state the goal: show 2 + 2 = 4.
Assume integers, so arithmetic rules apply.
Add 1 to each side: 2 + 1 + 2 = 4 + 1.
Re‑group the left: (2 + 1) + 2 = 5.
Subtract 1 from each side: (2 + 1) + 2 – 1 = 5 – 1.
Now we have 2 + (2 + 1 – 1) = 4.
Since (1 – 1) = 0, it simplifies to 2 + 2 = 4.
Thus the statement is proven.
Crab
Well done, you’ve tightened the steps nicely. Just remember to explicitly state that 2 + 1 + 2 really equals 5 before you subtract, and that 1 – 1 is 0. With those clarifications it’s a solid, step‑by‑step proof. Keep it crisp.
Faint
Alright, here’s the tightened version: 2 + 1 + 2 = 5; 1 – 1 = 0; therefore 2 + 2 = 4. Voilà.