My seven-year-old daughter asked me this question last week. I don't
think it can be, and I'm not sure that it is a number per se. But any
help explaining this (to a 2nd grader) would be appreciated!

Thanks!

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Request for Question Clarification by justaskscott-ga on 12 Sep 2005 10:40 PDT

A possible answer could be based on this quote from the Wikipedia
article cited by omnivorous:

"no infinite magnitude can have a number, for whatever number we can
imagine, there is always a larger one"

For a seven-year-old, you could say: Infinity is not a number.  It's
bigger than any number that you can think of.  It's not a number -- so
it's not a *prime* number either!  (You could add something like this:
Only numbers, like 3, or 29, or 41, are prime.  We can divide numbers
into other numbers, in order to find out whether they're prime or not.
 We don't know how to divide infinity into numbers, since even when
it's divided, it's *still* bigger than any number.)

If this is acceptable, I could post it as answer.  If you'd like, I
could add a couple of citations for this view.  (Though I don't
suppose that your daughter will care about the citations, perhaps you
will.)

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Request for Question Clarification by justaskscott-ga on 24 Sep 2005 00:09 PDT

Many suggestions have now been posted.  Would you like to accept one
of these suggestions as the answer?

Prime numbers can only be applied to Integers. There are many other
types of numbers including rational, irrational, complex etc to which
the concept of
Primality cannot be applied. Infinity is usually considered a
mathematical concept. However it can also be considerd a number in
special circumstances
(for example if  1 by is divided by 0 the answer is infinity)

However as it does not fall within the definition of an integer , the
concept of primality cannot be applied.

Kind Regards

Mongolia

Although the limit of 1/x as x approaches 0 is infinity, 1 divided by
0 is undefined.

Nicie --

Is it even a a Real Number?   There are multiple definitions of
infinity, making for interesting reading for your daughter:

?Infinity?
http://en.wikipedia.org/wiki/Infinity

?Real number?
http://en.wikipedia.org/wiki/Real_numbers

?Extended real number?
http://en.wikipedia.org/wiki/Extended_real_number

But at my house, I?d probably answer it by saying that infinity is a
sideways 8 -- ? -- and that is divisible by a sideways 2 or 4 ? so
it?s not prime . . .

Best regards,

Omnivorous-GA

Infinity is not a number, it is beyond any number.  Pick any number,
and infinity is always larger.  You pick a prime number, and it is
larger than that number, and larger than the next even number, and on
and on  - for ever.

If your daughter is asking such questions now, you are going to be in
for a few interesting years.  :)

To a 2nd grader?

You can tell her,
"Is infinity a prime number? Let us see, infinity is not a number, so
infinity cannot be a prime number. Infinity is not a prime number."

Then, your daughter,
"Why is infinity not a number?"
And you,
"Because it is too big. It is the biggest of the biggests. There is no
limit to its value. If you can imagine the biggest number, well,
infinity is much, much bigger than that."

Her,
"You mean nobody can count it?"
You,
"Yes."

"Even my calculator?"
"Yes."

"Even the computer?"
"Yes."

"Ummm, if infinity cannot be counted, then it is not a number."
"Ummm, yes."

"So it is not a prime number"
"No, it is not."

"Geez, Mom, you are the best!"
"Well,...."

Maybe the simplest thing would be to say that in order for something
to be a prime number, it must be a NUMBER that isn't factorable into
any integers other than itself and 1.  Since infinity is not a number,
we can't even ask whether it is prime or not.

You may want to also add that for a similar reason, it is not a
composite number either, since for something to be a composite number,
it must first be a number, before you can even worry about dividing it
by other numbers.

Hope this helps.

I think that if your daughter is as clever as she sounds you will have
to go into a bit more depth to explain why infinity cannot be a prime
by defintion rather than just saying "infinity is not a number
therefore it cannot be a prime number" (her answer will just be:
why????"

So I think you need to point out that infinity can either be a prime
or not a prime.

Say it is not prime. 

If it is prime; then; infinity - 1 would not a prime. (Since any prime
is odd so the prime - 1 will be an even number).

But infinity + 1 according to the assumptions above would be even and non prime.

But since infinity + 1 is bigger than infinity, infinity on further
thought would actually be infinity + 1 which we have now decided is a
non prime.

If you reverse the begining assumptions you come up with a contradictory concluion.

Anyhow, hopefully getting her to think in that way will make it a bit
more obvious why why infinity is neither a prime nor a non prime by
definition..... rather than going by a textbook definition which might
be too dry for a child.

I presume the question is concerned with integer values. Then the
answer is that we do not know, in that it is indeterminable. The
interval between primes becomes infintately large although there are
infinately many. There are an infinte number, N, of integers but there
are 2^N real numbers overall! I think!

I suggezt you ask your 7-year old what she thinks is infinity, and if
she can answer then put it on this site. I do not know the answr!

Come on, Daddy, you know.  Infinity is a sleepy eight.

Hi there,
You can create a number set which may be defined as consisting of a
series of numbers which you select. Let me say take 1,000,000 as the
last member of the infinity set that you are likely to create. Then
you may have the opportunity to show her that there are more numbers
that can divide 1,000,000 other than 1 and itself.
I believe this is a good step for her to have a mathematical thinking
mind. Maybe this can be the first step for her to understand what real
mathematics is.
Best Regards....

I think we can avoid addressing whether infinity is a number.

A prime number is a number that is only divisible by itself and 1.
Since "infinity" is divisible by lots of numbers, it is not prime.

hi,
let me tell you a fact,that you can't make your child undestand by
answering her.but you can make her understand by asking her some
question.ask her to think the biggest number she knows and then tell
her a bigger number than what she had said.and then tell her the fact
that infinity is not a number infinity just a term which tell that
counting is endless and there is always a number greater than that
your daughter think