Question on Infinite

[Turtle]

What about negative infinity and positive infinity?:confused:

 

chiral equivalents. :turtle:

[von Faulkenstein]

Non-Abelian or Abelian?:hihi:

[Jet2]

I'm lost.

[von Faulkenstein]

I got lost, too. I was studying the Standard Model where certain infinite numbers were being included in non-Abelian groups which were made up of ranges (that were considered extremely close together) still contained infinite numbers of fractions. This was being used in trying to find a unified field theory of the four forces--Em, strong/weak and gravity.

[Pyrotex]

"Chiral" is the property of being "handed"-as in left and right. Gloves are chiral, hats are not.

 

Positive infinity is merely (-1) times negative infinity, and vice versa. Not really chiral.

 

"Abelian" means a group (of numeric values, say, integers or real numbers) for which for all a and b members of the group, a*b = b*a. In other words, commutative. Though the real numbers (without zero) define an Abelian group, inifinity is NOT a real number, or in fact, a "number" in any mathematical sense. It is a concept. So infinity is NOT a member of any Abelian group that I am aware of. :)

[Turtle]

Positive infinity is merely (-1) times negative infinity, and vice versa. Not really chiral.:)

 

 

but on the other hand, it appears that way when dressed as a number line. :D :doh:

[Pyrotex]

but on the other hand, it appears that way when dressed as a number line. :hyper: :eek_big:

touche, turtle!

 

:hihi:

[Guest loarevalo]

Can any maths experts explain to me about this?

Are infinite large and infinite small the same?

 

Jet2 :)

 

Hello Again, It's been a while. I'm hoping with this to engage Jet2 into a sensible meditation about infinity. Hope you'll still read this:

 

To answer the question:Yes and No.

 

No:

Set Theory establishes there are diferent sizes of infinity, like

Aleph-0 : how many natural numbers are

Aleph-1> : how many real numbers are

and so on. We could call these, infinite small and infinite large, relatively.

 

Yes:

Well, these "alephs" are all characteristically infinite. For most practical purposes, infinite is infinite, no matter how you would distinguish one from another.

 

Formally, Mathematics says No. There are many sizes of infinity - a very important breaktrough in Mathematics through the twentieth century.

 

I would gladly discuss this further. if any have questions, bring them.:)

[Jet2]

Actually the original question I asked has a problem (or another question) in it...

It seems that I assume infinity is real and does exist. In fact with which I am not really sure...I think that should be the right question.

[Guest loarevalo]

Well, as of whether Infinity is real or not. :eek:It´s complicated. It depends in what context you´re dealing.

 

Formally, in foundation mathematics this is the number line:

 

0,1,2,3 . . . Aleph0, Aleph1 . . . AlephAleph . . .

 

These Alephs are infinites. There is no largest Aleph, or biggest infinity - it doesn´t stand a consistent definition. That´s interesting because the traditional definition of infinity has precisely been that: the ultimate number, a cap or lid on all the numbers. Since that didn´t stand up logically, infinity was not defined formally (it was taken as if it didn´t exist, and in fact, infinity does not exist among the real numbers. Calculus does not use infinity, just the idea of increase without limit). It remained as that until Cantor defined infinity using sets in the late 19th century.

 

I recommed you Jet2, to take any book, informal if you like so, about infinity or George Cantor - it will expand your vision. You can find them in any library.

[CraigD]

Formally, in foundation mathematics this is the number line:

 

0,1,2,3 . . . Aleph0, Aleph1 . . . AlephAleph . . .

This “transfinite number line” is neat way of describing the subject. :)

I recommed you Jet2, to take any book, informal if you like so, about infinity or George Cantor - it will expand your vision. You can find them in any library.

I agree. Also, many websites, such as he wikipedia article “transfinite number”, have good, brief overviews of the math and history of the math of infinity. Starting with a such summaries, you can find a lot of information by searching the web for the names and terms you encounter, though this lacks the neatly controlled rigor of a good textbook.

[snoopy]

I could explain infinite to you, but it would just take forever..

 

:eek:

:(

 

I was thinking the same thing.

 

But although infinity is a thorny subject, a mathematical object can be infinitely large or infinitely small.

 

You can always imagine a very large number and keep on going forever thinking up larger and larger numbers and the same can be said for decimal fractions between zero and one going infinitely smaller and smaller forever and ever.

 

Hope that helped JET2

cheers

:eek:

[Jet2]

Thank you all.

 

Actually the original question I asked has a problem (or another question) in it...

It seems that I assume infinity is real and does exist. In fact with which I am not really sure...I think that should be the right question.

 

I am wondering whether I should move this thread to the Philosophy Group??

[P3X491]

is there any difference between infinite +1 and infinite -1?

[Jet2]

Dear P3X491,

 

If we take Infinite or Infinity as a process, then the different is +1 and -1.

[Pyrotex]

Well, if we stick to mathematics, the standard math operators, +, -, *, / are not defined for infinity. Because infinity is not a member of the Real Numbers.

 

Infinity + 1 is not defined.

 

It's like the "pick" operator. "Picking" is defined for oranges and apples, but not for lakes or clouds.

[Qfwfq]

is there any difference between infinite +1 and infinite -1?

Well "obviously" the difference is 2... except there's a bit of subtlety behind it. If you mean:

 

[math]\lim_{x\rightarrow\infty}((x+1)-(x-1))[/math]

 

Then the answer is 2 but if you mean:

 

[math](A+1)-(B-1)[/math]

 

with A and B being two arbitrary infinite terms, then it's an indeterminate form, it only has an answer for some choices of the two terms. Subtle question: Suppose instead of the above example we consider:

 

[math]\lim_{x\rightarrow\infty}(x+1)-\lim_{x\rightarrow\infty}(x-1)[/math]

 

can we still say the answer is 2?