
#1
Apr3004, 03:56 PM

P: 122

Is [tex]\frac {1}{\infty} = 0[/tex] , or is it just infinitely close to 0?




#2
Apr3004, 03:58 PM

Sci Advisor
P: 5,942

= is correct, the other alternative is not too meaningful, unless you get involved with nonstandard analysis.




#3
Apr3004, 04:05 PM

P: 678





#4
Apr3004, 04:08 PM

Sci Advisor
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).




#5
Apr3004, 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...




#6
Apr3004, 04:48 PM

Sci Advisor
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.




#7
Apr3004, 10:00 PM

P: 122

No it isn't...Because that unit DOES exist. But by saying 1/inf = 0...we say it is nonexistant. In the same way, human population with respect to time would be 0 if the above statement were true. This is not so...




#8
Apr3004, 10:09 PM

Emeritus
Sci Advisor
PF Gold
P: 16,101

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. 



#9
Apr3004, 11:43 PM

Mentor
P: 7,292

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. 



#10
May104, 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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