On matters of infinity

This is an invited post
from Perhaps my doppelgänger,
that V is, with a cap on his E,
if you know what I mean.
With much enthusiasm,
writes, Mr. Victor,
on matters of infinity,
at barely an age of 20 or so.
So here you go,
without much delay,
fresh from the oven,
written by V, with a Cap on his E.

For you, a preposition,
About Infinities and Infinitesimals;
It is best if you don’t,
Rely on what is natural.
So let’s begin with something more orthodox.
Enter: Zeno’s Paradox
In case you don’t know (and I doubt it),
here is a tale of our mighty hero Achilles.
Tasked to run a full stadia,
or 176 meters, might I say.
So easy it seems,
for it was a myth among the Greeks.
It would take forever though,
For a rule must be observed.
To end, this simple task
Achilles must first run
Half of what is left.
This is a sure thing, you may say
But then, to complete the other half
He must do it again, but only
half of what is left, and other steps such as these.
“How may our hero end his quest?”
That’s the question: I can hear you ask.
I would like to introduce,
The new super task.
Hear, what I have for you,
And think about it for a minute or two
It could be confusing,
But it’s most certainly amusing.
If our mighty hero,
In each half mark waits
For a period,
That’s also the half of a given time
(Shall we Say, 2 minutes?)
To run the first half, he would wait a single minute
To the second half, he would wait half a minute
To the third half, he shall wait a fourth of a minute
And so on.
So my question is this:
If you can perform a fraction of a task
Infinitely fast
And the said task
Has no sure end
Would our brave hero, Achilles
(Mighty warrior that he is,
and a sharp mathematician perhaps?)
Find eventually
His deserved rest ?
An excel spreadsheet such as this
might come to your succour.
Good luck mon ami,
in the world of summations and other such things.



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