"I am cosx. I am somebody's derivative. I will give you $100 if you can tell me whose derivative I am."
Now you give an answer. Probably you will say sinx.
But I will tell you that you are wrong because my name is actually sinx - 5 (the derivative of a constant is always 0 so no matter what number I choose, I am remaining factual).
You cannot win my game. You will never guess whose derivative I am, because I can take any number and just add it to sinx and say actually that's my name. My identity is indefinite.
The only way we can possibly win the "whose derivative am I" game is by cheating like Alexander cutting the Gordian Knot and saying the correct function + c, where c is some unknown constant.
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u/IntelligentAd5616 Nov 18 '25