Associated Topics || Dr. Math Home || Search Dr. Math

### Eternity

```
Date: 12/30/97 at 21:32:59
From: Novie
Subject: Eternity

Hello Dr. Math,

If you must choose from two alternatives:

1. eternity
2. half of eternity

which is the best?

Can you match the eternity and the measurement?

Thank you very much.

Novie
```

```
Date: 12/31/97 at 17:25:03
From: Doctor Jerry
Subject: Re: Eternity

Hi Novie,

To answer such questions, one should have agreed upon the rules in
advance, but neither you nor I has the time to go through the theory
of cardinal numbers.

However, maybe I can answer by analogy. Would you rather have \$1 for
each counting number (1,2,3,4,...) or for each even number
(2,4,6,8,...)?  The second of these is something like "half of
eternity."

I think the answer to the above question is that I don't care, since
there are the same number of counting numbers as even counting
numbers.

This may be surprising to you. Here is the standard way of arguing:
Put the counting numbers in wastebasket 1 and the even counting
numbers in wastebasket 2. We're going to draw one object from each
wastebasket, tape them together, put them aside, and then repeat this
process. We're going to match them this way: I'll use (a,b) to mean
that a comes from wastebasket 1, b from wastebasket 2, and we've tied
them together.

(1,2),(2,4),(3,6),(4,8), and so on

You can see that we will have tied everything from both baskets
together, with nothing left in either basket. In this case, we say
that the two baskets have the same number of objects.

So, I'd say about the two eternities, it doesn't matter. There are the
same number of seconds in them.

-Doctor Jerry,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```

```
Date: 01/01/98 at 10:51:03
From: Novie
Subject: Re: Eternity

Dr.Math,

answer: Eternity and half of eternity are the same.

But why did you start with a number for eternity (not half of
eternity), presented by counting number (1,2,3 ...)?

We know that eternity has no beginning or end. In the case of half of
eternity we can say that wherever and whenever we are standing now is
half or 1/3, 1/4, 1/5 and so on of eternity. To our left is one part
of eternity, and the other is to our right.

Imagine we have two eternities and we fold one of them into two parts.
Because of the fold, an edge separates the left and right sides. The
other edge is still infinite (the edges for the left and right parts).
On the left we now have the ending number that reaches the folding
part, and on the right we have the starting number that begins with
the right folding part.

The other eternity is a whole without a beginning number. So there is
a space between eternity and half of eternity (or eternity divided by
any number).

So my theory of eternity is that if the eternity is a whole, it has no
beginning or end, but if we divide it by any number (like folding it)
we can have an end number on one side (the left side of the fold) and
a starting number on the other side (the right side of the fold).

My conclusion is that eternity and eternity divided by such a number
are not the same. Do you agree?

Novie
```

```
Date: 01/01/98 at 16:08:49
From: Doctor Jerry
Subject: Re: Eternity

Hello again Novie,

My argument was an attempt to give an idea about how mathematicians
count or compare infinite sets. They follow rules which are stated
ahead of time. Almost never do they enter into philosophical arguments
or discussions based on "common sense."  They know from experience
that there is no way of settling such questions.

I will make one more observation, one that somewhat fits with your
opinion that infinity has neither a beginning nor an end. The set R
of real numbers, including all negative numbers and all positive
numbers, is without beginning or end. Yet the set R has the same
cardinality (the same number of elements) as the set of real numbers
between -pi/2 and pi/2. This follows from the fact that the function

f(x )= arctan(x), -pi/2<x<pi/2

maps (-pi/2,pi/2) onto the set R.

-Doctor Jerry,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Analysis

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search