Gather around, boys and girls!
And I’ll sing you a song
Of a strange little paradox
Involving the number
Zero point . . .
Nine, nine, nine, nine,
Nine, nine, nine, nine,
Nine, nine, nine, nine,
Nine, nine, nine, nine,
Nine, nine, nine, nine,
Nine, nine, nine, nine,
Nine, nine, nine, nine,
Nine, nine, nine, nine . . . (etc.)
Does it equal one?
Does it equal one?
Does it equal one?
We all accept that when you find
The value of “one-third,”
You get a dec’mal point
And never-ending threes!
But triple that and what you get
Is slightly more absurd!
And it’s a fact on which
Not ev’ryone agrees . . .
On one hand, you have three groups
Of a third -- which should be fine!
It equals one! And it is clear
From whence that came!
But tripling the dec’mal gives
A repetend of nine --
And now a lot of folks
Aren’t sure that’s still the same!
Does it equal one?
<< Discussion >>
And does anybody really even care?
(Besides the eggheads?)
Nine, nine, nine, nine,
Nine, nine, nine, nine,
Nine, nine, nine, nine,
Nine, nine, nine, nine,
Nine, nine, nine, nine,
Nine, nine, nine, nine,
Nine, nine, nine, nine,
Nine, nine, nine, nine . . . (etc.)
Now, if you’re having troubles
‘Cause you think there’ll be a gap
That will prevent the final nine
From reaching “one” --
It’s really not a problem,
You’ve just fallen in the trap
Of not remembering
This number’s never done!
It’s infinite! It doesn’t leave a gap
Or have an end!
No “final nine”!
It just keeps going right on through!
It represents a limit!
Not a sequence or a trend!
And there there are many ways
To prove that this is true!
So it equals one!
<< Discussion >>
But I’m still afraid that no one really cares!
(Except the math geeks!)
Nine, nine, nine, nine,
Nine, nine, nine, nine,
Nine, nine, nine, nine,
Nine, nine, nine, nine,
Nine, nine, nine, nine,
Nine, nine, nine, nine,
Nine, nine, nine, nine,
Nine, nine, nine, nine . . . (etc.)
Now I know that not ev’ryone
Will find this really cool.
There may be others
Who are feeling somewhat bored.
But think of all the things
You never got to learn in school
And all the paradoxes
Yet to be explored!
‘Cause Kruskal has a way
To show a number that’s surreal;
That is unique
In an iota’s worth of space!
And Zeno says Achilles
Has his own “Achilles heel,”
‘Cause he can never beat
A tortoise in a race!
<< Hmmm... >>
(Seems like he’d have won!)
<< Discussion >>
