# Answer help: Is there a mathematical system that would allow any problems to be solved between different versions of infinite? - Help.com

## Is there a mathematical system that would allow any problems to be solved between different versions of infinite?

Like “what is the difference from 111…2.0
to 111…8.0?

I imagine that the answer would be 1111…0.0

or maybe 111…1.0 or 111…10.0

and I realize that it’s quite probably imposible with a 10 digit numbering system, I am assuming. If no answers seem logical, do you think that there is a number system that would work for it? It seems to me that an infinite number system would easily equate that operation, but I haven’t spent much time with such a concept and I have done no research on it either.

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### Replies (17)

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I’m not sure how to interpret those numbers. Then again, I dont run into them very often :) What does that format represent?

Are you saying like 11111111… base 2
compared to
11111111… base 8?

the “…” represents infinite

Ok, so your 2.0 and 8.0 are coefficients? I’m just not sure how to read

111…2.0
111…8.0

or should I say ***…6, where *** = any three digits and … = the infinite repetition of ***. Such as 234234234234234234234234… or 234234234234234234234234…1.0

where 1.0 is at the end of infinite 234 repeating.

Ok, I see what you’re saying.

6.0

I think everything else cancels.

Ok, I don’t know if this makes sense, but I would convert each of the infinite numbers to an expression that uses a common variable.

Like, make x = 111…2.0

Then the first number would be x, and the second number would be x+6.0

Do all the operations, and then substitute x back in if it’s still there

I, too think that it should be 6, but I’ve recently been told that it was impossible to have a number past infinite. It was when I was reading how it is said that 1 and .999 repeating are the same number and separately how if something was 99.999…%. I want to find out the kind of math that would be involved to even communicate that .000…1 percent.

I’ve heard that it’s impossible, but I can’t shake feeling like it should exist somehow, so I started wondering about different number systems. Like binary, or infinite numbered number systems.

Hmmm, that does seem strange. The one that is really not sitting quite right with me is “The Grand Hotel”, which claims more guests can fit in a hotel with all the rooms already occupied:
http://en.wikipedia.org/wiki/Hilbert’…

Here is some other stuff that relates to it:
http://en.wikipedia.org/wiki/Cardinality
http://en.wikipedia.org/wiki/Aleph_nu…

There is actually an article on 0.999…
http://en.wikipedia.org/wiki/0.999

And lastly, here’s an interesting bit:
http://en.wikipedia.org/wiki/Zeno’s_p…

syrilram wrote:
or should I say ***…6, where *** = any three digits and … = the infinite repetition of ***. Such as 234234234234234234234234… or 234234234234234234234234…1.0

where 1.0 is at the end of infinite 234 repeating.

huh? If 1.0 is at the end of that number then 234 does not infinitely repeat.

love4tacobell wrote:

syrilram wrote:
or should I say ***…6, where *** = any three digits and … = the infinite repetition of ***. Such as 234234234234234234234234… or 234234234234234234234234…1.0

where 1.0 is at the end of infinite 234 repeating.

huh? If 1.0 is at the end of that number then 234 does not infinitely repeat.

I think it repeats infinitely, it’s just bounded on the right hand side by 1.0. There are no other places where it fixes a decimal point, so the 234234… grows out infinitely to the left.

Like …2342342341.0

*decimal place

Grows out infinitely to the left? That doesn’t make much sense to me, seeing that the number system we use goes from left to right, not right to left…

Anyway, since the number has an end (1.0) it is NOT infinite. It doesn’t matter if it repeats infinitely at the left because the number at the end would make it a finite number. OP is basically talking a number that is infinite and finite at the same time, which doesn’t make sense. the number is finite, by definition.

@love4tacobell

I think you are confusing “irrational” and “infinite”.

I think you would be right that it’s not irrational, but it definitely is infinite, because for any decimal placeholder you choose, it has a digit to the left of that (with a factor of 10 more magnitude). So you can’t pin it down as finite.

It’s basically the sum of an infinite number of integers (corresponding to each digit in the number), and such a sum is also infinite.

I actually meant more like, there is a beginning number on the left and then the middle is infinite and the right is finite. so 3…6.0

… is infinite

I can certainly understand that the consensus is that that is impossible, though, I don’t see why, that is beside the question. What I want to find out is if there is a number system that this would work in. Such as a base-infinite or maybe base-1 numbering system or if that even makes any difference.

I think a numbering system must be at least base 2, as in most computers.

I could believe the .99999… = 1 thing (as strange as that sounds), but still not sure about the first question with the difference of those two numbers.

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