A mathemajical story

 

Once upon a time (1/t), pretty little Polly Nomial was strolling across a field of vectors when she came across 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.  Quite suddenly three branches of a hyperbola touched her at a single point.  She oscillated violently, lost all sense of directrix and went completely divergent.  As she reached a turning point, she tripped over a square root that was protruding from the erf and plunged headlong down a steep gradient.  When she was differentiated once more she found herself, apparently alone, in a non-Euclidian space.

 

She was being watched however.  That smooth operator Curly Pi was lurking inner product.  AS his eyes devoured her curves a singular expression covered his face.  Was she still convergent, he wondered?  He decided to integrate improperly at once.

 

Hearing a vulgar fraction behind her, Polly turned 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.

 

Eureka, she cried.

Ho, Ho, he said.  What a symmetric little polynomial you are.  I can see that you are absolutely bubbling over with secs

O Sir, she protested, keep away from me.  I have not got my brackets on.

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

i, i, she thought.  Perhaps he is homogeneous then.

What order are you, the brute demanded.

Seventeen, replied Polly.

Curly leered.  I suppose you have never been operated on yet, he said.

Of course not, Polly cried indignantly.  I am absolutely convergent.

Come then, said Curly.  Let us go off to a decimal place I know and I will take you to the limit.

Never, gasped Polly.

EXCHLFT he swore, using the vilest oath he knew. 

 

His patience cancelled, he coshed her coefficient with a log until she was powerless and removed her discontinuities.  He stared at her significant figure 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.   He integrated by parts.  He performed partial integration.  The complex beast even got round to performing a contour integration.  What an indignity.  To be multiple connected on her first integration.  Curly went on operating until he was completely factorised.

 

When Polly got home that evening her mother noticed that she had been truncated in several places.  But it was too late to differentiate now.  As the months went by Polly increased monotonically.  Finally she generated a small but pathological function, which left surds all over the place until she was driven to subtraction.

 

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

 

The End.