- #1
Hippasos
- 75
- 0
Let n be any number.
infinity + n = infinity
n = infinity - infinity
n = undefined
!...?
infinity + n = infinity
n = infinity - infinity
n = undefined
!...?
Hippasos said:Let n be any number.
infinity + n = infinity
n = infinity - infinity
n = undefined
!...?
mgb_phys said:If you're a mathematician - yes it's undefined
If you're a physicist then it can be zero or infinity depending on which makes your theory work!
Hippasos said:Let n be any number.
infinity + n = infinity
n = infinity - infinity
n = undefined
!...?
NEITHER statement makes any sense until you specify what what number system you are working in. "Infinity" itself is not defined in either the real number field nor the complex number field and so neither statement makes any sense in them. There are several different ways to extend the number systems to include "infinity" and operations involving "infinity". Those statements may or may not make sense depending on the system.al-mahed said:the second statement doesn't make any sense, am I right?
Hippasos said:Let n be any number.
infinity + n = infinity
n = infinity - infinity
n = undefined
!...?
al-mahed said:Could you explain?
Gib Z said:It was a joke, poking fun at the way physicists do mathematics.
yasiru89 said:You do realize mgb phys that your little tricks of trade have extrapolated from the mathematical theory of limits instead of adding to it? In functional form an expression of the form [tex] \infty - \infty [/tex] may be reduced to the form [tex]\frac{\infty}{\infty}[/tex] and evaluated by a method such as l'Hopital's rule(as long as putting into the required form does not make an answer obvious) to obtain a finite, infinite or null answer.
The space being worked on may be altered to fit the theory and methods of renormalisation introduced to deal with these forms...
yasiru89 said:Say some expression is of the form [tex] \infty - \infty [/tex] and defined by a limit on the variable(say x approaches a) by [tex] f(x) - g(x) [/tex]
Since this may be changed into,
[tex] g(x).[f(x)/g(x) - 1] [/tex]
We can deal with this case using l'Hopital's rule. This works when the limit exists of course but some 'physical' theories require more, the most famous being Quantum Field theory I believe. Then we work with alternate definitions and methods like going through extra dimensions to drop off infinities along the way. In such ways we are left with sensational results like [tex] \prod_{p} p = 4\pi^{2} [/tex] (product over all primes denoted)
Well, in my limited experience and knowledge, I would say then:nicksauce said:Let n = be any number
cat + n = blue
n = cat - blue
n = undefined ?
Infinity is not a real number, so you cannot perform operations like infinity + n, just like you cannot perform operations like cat + n, or n = cat - blue.
No need to be confused. Just accept the fact that infinity is just a concept not a number sinced there is no such thing as a biggest or smallest number. Only if you accept that can you appreciate the beauty of mathematics. Also you can liken an infinite series that has a limit as the sum to an endless do loop in which one gets closer and closer to the answer without actually reaching it, except that you can see the what the answer should be by looking at the computer screen.Hippasos said:Well, in my limited experience and knowledge, I would say then:
Arithmetics - as I know it - is a cat with a leg of an elephant(<-infinity) - detached or not I don't know...
Still confused...
Gib Z said:Not even physicists (at least at the level of those who create decent theories) have such terrible mathematics that they believe that product. Of course they know they are using some different operator. Perhaps this operators gives the right product for where the product of the usual operator exists, but its still different.
Gib Z said:The only other poster who was hinting towards rapidity of divergence was MaWM, who is also misinterpreting the question. If you notice everyone elses posts, you'll realize we weren't even talking about functions, order of divergence or anything very analytical at all.
Gib Z said:PS. Something can't be half dead.
mikepr@mac.co said:n + infinity does not just give you infinity back again, it gives you a different (ever so slightly larger) infinity.
mikepr@mac.co said:i'm not making up my own number system. the example i used to demonstrate different kinds of infinities is over 100 years old. to be sure it doesn't have anything to do with this topic, other than if you can understand it, you can easily understand that in the orginal poster's example, n is still going to be n.
Hurkyl said:CRGreathouse knows what he's talking about.
mikepr@mac.co said:in n + x = w, it really doesn't matter what x is or if w is defined. if you do the opposite operation knowing the definition of n, you'll always get n back.
mikepr@mac.co said:that'd be cantor. some quick links from google:
http://scidiv.bcc.ctc.edu/Math/diag.html
http://people.bath.ac.uk/jp253/Project.html
http://www.sciam.com/article.cfm?id=strange-but-true-infinity-comes-in-different-sizes
http://mathcentral.uregina.ca/QQ/database/QQ.09.03/plober1.html
al-mahed said:I think as infinity is not a defined amount (you cannot count it), the ordinary algebra is not applicable
What do you mean by "amount"? You would be correct to assert that there are no infinite natural numbers, nor are there infinite real numbers.al-mahed said:I think as infinity is not a defined amount (you cannot count it)
Of course -- different number systems require different arithmetic. e.g. we cannot use natural number arithmetic when working with the cardinal numbers, because natural number arithmetic doesn't tell us anything about infinite cardinals.the ordinary algebra is not applicable
It can be hard to explain something new to someone. But it's much harder to explain something to someone who has already seen it, but learned it wrongly.CRGreathouse said:Thanks, Hurkyl. Sometimes I wonder if I'm explaining myself poorly... wouldn't be the first time.
Hurkyl said:It can be hard to explain something new to someone. But it's much harder to explain something to someone who has already seen it, but learned it wrongly.
Hurkyl said:What do you mean by "amount"? You would be correct to assert that there are no infinite natural numbers, nor are there infinite real numbers.