RE: indeterminate forms.

What is the correct evaluation of infinity/0 ? I've checked three different math sites. One says definitively, that infinity/0 is "not" possible. Another states that infinity/0 is one of the indeterminate forms having a large range of different values. The last reasons that infinity/0 "is" equal to infinity, ie:

Suppose you set x=0/0 and then multiply both sides by 0. Then (0 x)=0 is true for most any x-- indeterminant. Now set x= infinity/0. Then (0 x)= infinity can only be true if x is infinite.

So, what is the real answer to infinity/0 or at least the most widely accepted answer in the global mathematical community ?



Working with infinity/0 is a delicate matter. First of all the operation of division of s by t to yield s/t is only valid if s and t are numbers, and t is not zero. Thus infinity/0 is a problem both because infinity is not a number and because division by zero is not allowed. The usual interpretation of infinity/0 is "What happens to the fraction s/t as s approaches infinity and t approaches zero?" The answer "infinity" is close, but it depends on which 'picture' of infinity you have.
   Are there two infinities, a +infinity and a -infinity? If yes, then you have to check how you approach 0. Do you approach zero through positive values (we write this 0+) or do you approach zero through negative values (we write this 0-)?

Given this set-up:

+infinity/0+ = + infinity.
+infinity / 0- = - infinity
-infinity/0+ = - infinity
-infinity/0- = + infinity.

   If you are thinking of only one infinity, where the line appears more like a circle closing up to a single infinity from both 'ends', then there is only one infinity (+infinity= -infinity) and infinity/0 = infinity.

Walter and Harley

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