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### Infinity over Infinity

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Date: 4/10/96 at 18:50:50
From: "Jeremy Vigneault"
Subject: Infinity question

Dear Dr. Math,

I have a question maybe you can answer.  My electronics teacher
and I are having a disagreement.  He says that Infinity divided by
Infinity equals one.  I most certainly disagree; I say that
infinity over infinity is indeterminate, because infinity is a
discrepancy?
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Date: 4/12/96 at 21:36:13
From: Doctor Syd
Subject: Re: Infinity question

Dear Jeremy,

Good work!  You are correct.  Many people are confused by
infinity; you are right that is a concept and not a number the way
that 28 is a number.  There are sort of some different "sizes" of
infinities, so this means that a quotient that looks like infinity
over infinity can sometimes be  a real number, and sometimes it is
just infinity.

following problem:

What is the limit as x approaches infinity of the expression
x^2/(x-5)?   If you "plug in" infinity for x in this expression
you getinfinity over infinity, but if you apply L'Hopital's Rule,
you see the the numerator dominates the denominator (you can see
this without L'Hopital's Rule, too:  x^2 gets big a lot faster
than x does, right?), so the limit as x approaches infinity will
be infinity, not one.

Good question!  Hope this helped some.

-Doctor Syd,  The Math Forum

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Associated Topics:
High School Analysis

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