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Just want to clear this up

by Warr
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Apr30-04, 03:56 PM
P: 122
Is [tex]\frac {1}{\infty} = 0[/tex] , or is it just infinitely close to 0?
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Apr30-04, 03:58 PM
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= is correct, the other alternative is not too meaningful, unless you get involved with non-standard analysis.
Apr30-04, 04:05 PM
P: 678
Quote Quote by mathman
= is correct, the other alternative is not too meaningful, unless you get involved with non-standard analysis.
Unless you're using non-standard analysis I don't think the statement [itex]\frac{1}{\infty}=0[/itex] is even meaningful.

Apr30-04, 04:08 PM
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PF Gold
P: 2,226
Just want to clear this up

Well, you could say 1/x -> 0 as x tends to infinity (though that obviously doesn'; mean 1/inifnity = 0 especially when infinity isn't even a number).
Apr30-04, 04:09 PM
P: 122
Lets say there is 1 unit of something in an infinitely large area...then would you say = ? Because then that says that the unit doesn't even exist...
Apr30-04, 04:48 PM
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PF Gold
P: 2,226
No in that situation all we would be saying is that it would be meaningless to talk about the ratio of the area to the unit area.
Apr30-04, 10:00 PM
P: 122
No it isn't...Because that unit DOES exist. But by saying 1/inf = 0...we say it is non-existant. In the same way, human population with respect to time would be 0 if the above statement were true. This is not so...
Apr30-04, 10:09 PM
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PF Gold
Hurkyl's Avatar
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1/∞ doesn't have a "standard" meaning; in some systems where infinite numbers are defined, division doesn't exist. In some others, 1/∞ is some infinitessimal positive nonzero number. In others, 1/∞=0.

If you're thinking of ∞ as that "big number that sits at the positive end of the real numbers", then you probably mean to use the extended real numbers, where 1/∞ is defined to be equal to zero.
Apr30-04, 11:43 PM
Integral's Avatar
P: 7,315
In my books when infinity is defined as an extension to the Real number line, operations on infinity are also defined, included with these definitions is:

[tex] \frac 1 \infty = 0 [/tex]

This is a very specific definition for a very specific application ie the real numbers. If you attempt to apply this definition out of context your results may vary.
May1-04, 08:22 PM
P: 617
I always thought it meant infinitely close to zero, and that’s why the delta at the end of an integral doesn’t yield zero results, because the delta doesn’t actually = zero, just something infinitely small.

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