IMPURE MATHEMATICS 

Once upon a time (l/t) pretty little Polly Nomial
was strolling across a field of vectors when she
came to the boundary 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, was feeling particularly badly
behaved and ignored this condition on the basis
that it was insufficient, and made her way
amongst the complex elements. 

Rows and columns closed in on her from all
sides. Tangents approached her surface. She
became tensor and tensor. Quite suddenly, two
branches of a hyperbola touched her at a single
point. She oscilated violently, lost all sense of
directrix and went completely divergent. She
tripped over a square root, and plunged headlong
down a steep gradient. When she rounded off
once more, she found herself inverted, apparently 
alone, in a non-Euclidean field. (Would you 
believe space?) 

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

Hearing a common fraction behind her, Polly
rotated and saw Curly Pi approaching with his
power series extrapolated. She could see at once
by his degenerate conic and his dissipative terms
that he was bent on no good. 

"Arcsinh!" she gasped. 

"Hoho," he said. "What a symmetric little
asymptote you have. I can see that your angles
have a lot 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. What
order are you?" 

"Seventeen," replied Polly. 

Curly leered, "I suppose you've never been
operated on." 

"Of course not," replied Polly quite proudly, "I'm
completely convergent." 

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


"Never!" gasped Polly. 

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

There was no mercy because Curly was a
heavyside operator. Curly's radius squared itself:
Polly's loci quivered. He integrated by parts. He
integrated by partial fractions. The complex beast
even went all the way around and did a contour
integration. What an indignity--to be multiply
connected on her first integration! Curly went
right on operating until he had sgisfied her
hypotheses. 

When Polly got home that night, her mother
noticed that she was no longer continuous but
had been truncated in several places. But it was
too late to differentiate now. As the months went
by, Polly's denominator increased monotonically.

Finally, she went to the L'Hospital and generated
a small but pathological function. 

The moral of our sad story is this: If you want to
keep your convergence, never allow a single
degree of freedom. 

Auntie Derivative. 

Rated x^2 No one under 360 degrees admitted.