Once upon a time (1/t), pretty little Polly Nomial was strolling across a
field of vectors when she came to the edge of a singularly large matrix.
Now Polly was convergent and her mother had made it an absolute condition
that she must never enter such an array without her brackets on. Polly,
however, who had changed her variables that morning and was feeling
particularly badly behaved, ignored this condition on the grounds that it
was insufficient, and made her way in amongst the complex elements.

Rows and columns enveloped her on all sides. Tangents approached her
surface. She became tensor and tensor. Suddenly two branches of a hyperbola
touched her at a single point. She oscillated violently, lost all sense of
direction, and went completely divergent. As she reached a turning point she
tripped over a square root that was protruding from the erf, and she plunged
headlong down a steep gradient. When she was differentiated once more, she
found herself, apparently alone, in a non-Euclidean space.

She was being watched, however. That smooth operator, Curly Pi, was lurking
inner product. As he numerically analyzed her, his eyes devoured her
curvilinear coordinates, and a singular expression crossed his face. Was she
still convergent, he wondered. He decided to integrate improperly at once.

Hearing a common fraction behind her, Polly rotated and saw Curly
approaching her with his power series expanding. She could see by his
degenerate conic that he was up to no good.

"What a symmetric little polynomial you are," he said. "I can see that your
angles have lots of secs."

"Oh sir," she protested, "keep away from me. I haven't got my brackets on."

"Calm yourself, my dear", said our suave operator. "Your fears are purely
imaginary."

"I, i," she thought. "Perhaps he's homogeneous."

"What order are you?" the brute demanded.

"Seventeen," replied Polly.

"I suppose you've never been operated on?"

"Of course not," Polly cried indignantly. "I'm absolutely convergent."

"Come, come," said Curly. "Let's go off to a decimal place, and I'll take
you to the limit!"

"Never!" gasped Polly.

"Abscissa!" he swore, using the vilest oath he knew. His patience was gone.
Coshing her over the head with a log until she was powerless, Curly removed
her discontinuities. He stared at her significant places and began smoothing
her points of inflection. Poor Polly. She felt his hand tending to her
asymptotic limit. Her convergence would soon be gone forever.

There was no mercy, for Curly was a heavyside operator. Curly's radius
squared itself. Polly's loci quivered. He integrated by parts. He integrated
by partial fractions. After he cofactored, he performed Runge-Kutta on her.
The complex beast even went all the way around and did a contour
integration. Curly went on operating until he satisfied her hypothesis, then
he exponentiated and became completely orthogonal.

When Polly got home that night her mother noticed that she was no longer
piecewise continuous, but had been truncated in several places. As the
months went by, Polly's denominator increased monotonically. Finally she
went to l'Hospital and generated a small but pathological function which
left little surds all over the place and drove Polly to deviation.

The moral of the story is, "If you want to keep your expressions convergent,
never allow them a single degree of freedom."