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Reasons why infinity hasn't been implemented into modern math 
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#1
Jul508, 09:59 PM

P: 267

I don't really understand why it hasn't been numerically added into modern math. I mean, we make all kinds of properties for zero, but we can't make properties for infinity? It gets messy from time to time, but we could define everything strictly so that it still works algebraically.
Example: (quoted from http://mathforum.org/dr.math/faq/faq.divideby0.html) 5/0 = [tex]\infty[/tex] 5 = 0*[tex]\infty[/tex] Multiplicative property of 0. 5=0 WRONG! If we defined [tex]\infty[/tex] numerically: 5/0 = 1/0 5 = 0/0 We then, could define 0/0 as truly undefined, or all real numbers, or some other name. I don't think we need to classify something as undefined, or anything for that matter, unless it is 0/0, 0^0, [tex]\infty^\infty[/tex] etc. As for infinity, it should be implemented carefully into our modern math. Now it's time for you to post "Reasons why infinity hasn't been implemented into modern math." 


#2
Jul508, 11:39 PM

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Infinity is present everywhere in modern math. From simple implementations such as the extended real numbers to the more abstract cardinal and exotic ordinal numbers.



#3
Jul608, 12:23 AM

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Don't forget the projective reals!



#4
Jul608, 04:56 AM

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Reasons why infinity hasn't been implemented into modern math
Or indeed the projective anything, the compactifications of spaces, the Riemann sphere, the theory of poles and singularities going back hundred+ years, Laurent series, Mobius transformations,....



#5
Jul608, 12:06 PM

P: 267

I'm talking numerically, 1/0. You won't ever see its notation in a function etc...



#6
Jul608, 12:17 PM

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You don't see an infinite integer simply because the ring of integers doesn't contain such a thing. The ring of integers doesn't contain 1/2 either. 


#7
Jul608, 12:48 PM

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#8
Jul608, 06:38 PM

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Actually, I'm pretty tired of the word "infinity". A good tenth of the posts on these math forums could be avoided if posters instead named the sort of infinite number they were thinking about. The onepoint compactification of the reals? Aleph2? Epsilonnaught? The IEEE +Infinity?



#9
Jul608, 09:58 PM

P: 72

location.reimannsphere(santa) ???



#10
Jul608, 10:14 PM

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#11
Jul708, 04:32 AM

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It doesn't 'define infinity as undefined' (which is a contradiction in terms). It merely, and correctly, states that you can't cancel off zeroes in multiplicative expressions.



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Jul708, 05:04 AM

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#13
Jul708, 08:20 AM

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Well, epkid08, your post has been answered: mathematics does 'implement infinity'. Allow me to suggest that, before you continue ranting, you spend some time studying mathematics so as to gain an understanding both of how mathematics works and how the notion of infinite is treated and used in mathematics.
Incidentally, your comment on zero is unfounded. It is so incredibly useful that natural languages have evolved to give it special treatment  the difference between 'zero' and 'not zero' is quite deeply ingrained in grammar. (Apparently so deeply that some people have difficulty comprehending how they could be united into a notion of 'quantity') Grammar can also split the latter case into 'one' and 'more than one', but not in such an essential way. (There is some limited direct linguistic support for larger quantities, but going beyond one usually entails using ordinal or cardinal numbers) 


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Jul708, 09:09 AM

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#15
Jul708, 09:55 AM

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#16
Jul708, 10:27 AM

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#17
Jul708, 01:27 PM

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My main problem is that lowlevel algebra defines infinity as undefined, when in reality we have no reason to classify it so. Zero is also a special class of number, which has its limited uses, but we find the time to define that.
We call it undefined for the same reason we tell gradeschoolers they can't sqaure root negative numbers  it'd confuse the hell out of them and it's offtopic. When their minds are ripe, and the contexts of our discussion is proper, these concepts are introduced. Crawl before you can walk. Oh, and, surprise, some infinities are bigger than others and we can divide by zero. Hehehe. 


#18
Jul708, 02:40 PM

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