# Thread: Is a number preceding infinity, finite?

1. ## Is a number preceding infinity, finite?

Hi,

I'm not sure if this is the right section, but I'm talking about numbers .

The questions is as written in the title: Is a number preceding infinity, finite?

2. ## Re: Is a number preceding infinity, finite?

Is "infinity" a place?

"Infinity" - 1 remains greater than any value you can suggest (without referencing "infinity").

3. ## Re: Is a number preceding infinity, finite?

If infinity is the largest number that could ever be, then surely anything less must be finite...

4. ## Re: Is a number preceding infinity, finite?

define "precede" and "infinity".

the reaon i make this request is this:

supposing you defined infinity to be the number of (distinct) real numbers, and defined "precede" to mean, any number strictly less than the number of real numbers.

the number of rational numbers is strictly less than the number of real numbers, but this number is not finite.

it turns out there are different "kinds" of infinity, and they act a bit differently. the "smallest" infinity is used often enough to get its own name, $\omega$.

this is the number of natural numbers (which turns out, strangely enough, to be the same number as the number of integers, AND the number of rational numbers. infinte things behave very strangely).

it's safe to say that if n < $\omega$, then n is finite (sometimes this is even written as n < $\infty$).

5. ## Re: Is a number preceding infinity, finite?

Originally Posted by webguy
If infinity is the largest number that could ever be, then surely anything less must be finite...
Infinity is not a number unless you start operating in the system of extended reals (or similar systems) but you have not met such so it is not a number.

CB

6. ## Re: Is a number preceding infinity, finite?

for a not-very-technical view of this, check out this video series:

Horizon - To infinity and Beyond part 1 of 6 - YouTube

7. ## Re: Is a number preceding infinity, finite?

So, in order for infinity to be infinite it must have infinite predecessors? Hence, anything preceding infinity is infinite? I suppose infinity should be treated differently since there is no border between something being finite and something being infinite. It is not as though I can say finiteN+1=infinity because unlike infinity both finiteN and 1 are finite.

Have I finally made sense of the situation?

8. ## Re: Is a number preceding infinity, finite?

No, you're just talking circles. You need a clear defintion before you think you have achieved something.

9. ## Re: Is a number preceding infinity, finite?

OP,

I believe that you are asking a set theoretical question. The smallest level of infinity is w=|N| where N is the set of natural numbers. w has no immediate predecessor because n<w for each natural number n. However, there are proper subsets of N that have size w. For example, the set E of even natural numbers has size w. That is , there is a one-to-one correspondence between N and E, for example {(n,2n)|n in N}.