I walked along my sequence on a silvery moonlit night,
Though the fog was thick and the cluster points, dense, I could see the proof, the fearsome dragon, in sight.
Ahead of me, I could hear it sleeping, its breathing steady and slow.
“Aha! I shall find its limit”, I thought. Clutching my weapons of analysis,
I charged forward, shouting, “I fix epsilon greater than 0!”
But alas, the calculus beast was waiting and it emerged with a thunderous roar.
With claws that diverged to infinity, the roguish beast pounced,
thirsty for a mathematician’s blood and gore.
I punched it with Cauchy Criterion, and tailored its Taylor series with quickened haste,
Flanked it with Bolzano-Weierstrass theorem, and applied the MVT and IVT for taste.
But alas, its derivatives were unbounded, and it escaped my delta neighbourhood.
Staring at its complexity, I thought with fear,
“For the love of Analysis, will no one prove this for good?”
And then, the fog is lifted and a radiant beam of white light shines forth.
Out from the mist, with sword in hand,
Steps in the one and only, Artem Pulemotov.
He looks at the beast and laughs, “you’re trivial! I shall give you an N to all ends!”
He lunges forward, wrangling with the Taylor remainder term,
Under mathematical rigour, the beast was condemned.
As it tried to escape, Artem grabbed it tightly and held it under comparison.
After stripping its fraction and reducing it with triangle inequality,
he pins his sword down, “I claim you are less than epsilon!”
That does it! QED! The dragon is defeated! He shall no longer be a threat.
And Artem? Well, he says nothing but rides off
On his scooter into the glorious sunset.