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 >>