- Infinity has never clearly explained to me while I was in school. Maybe you

guys can help me. The following are a list of True or False question.

True or False:

1) Infinity is a number.

2) Infinity is an odd number.

3) Infinity is a prime number.

Thanks,

--kent - At 07:49 PM 11/30/2001 +0000, Kent Nguyen wrote:
>Infinity has never clearly explained to me while I was in school. Maybe you

Yes, but it isn't an integer or real number.

>guys can help me. The following are a list of True or False question.

>

>True or False:

>1) Infinity is a number.

http://mathworld.wolfram.com/Infinity.html

>2) Infinity is an odd number.

False.

>3) Infinity is a prime number.

False.

+---------------------------------------------------------+

| Jud McCranie |

| |

| Programming Achieved with Structure, Clarity, And Logic |

+---------------------------------------------------------+ - At 07:49 PM 11/30/01 +0000, Kent Nguyen wrote:
>Infinity has never clearly explained to me while I was in school. Maybe you

Depends on your definition of numbers (my favorite is in Conways "on

>guys can help me. The following are a list of True or False question.

>

>True or False:

>1) Infinity is a number.

numbers and games").

Infinity is not an integer. It is a member of a set of numbers called the

"extended reals (+infinity,

and -infinity)". It is many numbers if you are speaking of the cardinal

numbers (sizes of sets).

>2) Infinity is an odd number.

No, it is not an integer.

>3) Infinity is a prime number.

No, it is not an integer.

- --- In primenumbers@y..., Chris Caldwell <caldwell@u...> wrote:
> >2) Infinity is an odd number.

Both of the statements Chris made are true by definition.

>

> No, it is not an integer.

>

> >3) Infinity is a prime number.

>

> No, it is not an integer.

However, this leads to an interesting question.

What is the "proper" way to say (for instance):

1. Compute the sum of 1/p^2 as p ranges over the prime numbers

from 2 to infinity.

or

2. Compute the product of 1+(1/x^2) as x ranges over the

odd numbers from 1 to infinity.

I think these are both proper and it is understood that the

"infinity" reference is not to an actual number but is rather

a succinct way of stating that the range goes on without bound.

However, I could understand how someone reading (1) or (2) above

might think that infinity is a prime number or an odd number... - On Fri, 30 November 2001, jack@... wrote:
> --- In primenumbers@y..., Chris Caldwell <caldwell@u...> wrote:

as p ranges over the unbounded set of prime numbers greater than or equal to 2.

> > >2) Infinity is an odd number.

> >

> > No, it is not an integer.

> >

> > >3) Infinity is a prime number.

> >

> > No, it is not an integer.

>

> Both of the statements Chris made are true by definition.

>

> However, this leads to an interesting question.

>

> What is the "proper" way to say (for instance):

>

> 1. Compute the sum of 1/p^2 as p ranges over the prime numbers

> from 2 to infinity.

?

Which certainly could be shortened without any wild ambiguity.

> or

... unbounded set of odd numbers greater than or equal to 1.

>

> 2. Compute the product of 1+(1/x^2) as x ranges over the

> odd numbers from 1 to infinity.

> I think these are both proper and it is understood that the

Infinity as a bound => no finite bound => no bound

> "infinity" reference is not to an actual number but is rather

> a succinct way of stating that the range goes on without bound.

> However, I could understand how someone reading (1) or (2) above

You don't explicitly say whether the set is open or closed. Why should someone assume a closed set, and thus an included upper bound, rather than a half-open set, with an excluded upper bound? The danger is more that of people infering something erroneous from something not said, rather than misinterpreting something actually said. Errors like that are always harder to prevent. You can't exclude every possible inference, I'm sure.

> might think that infinity is a prime number or an odd number...

<JSH> What ring were you working in, again? </JSH>

Phil

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