Adding InfinityDate: 06/25/2003 at 11:33:13 From: Joshua Calais Subject: Infinity What is -infinity plus infinity? This question was our class discussion today in Calculus II. The discussion was whether it equals 0 or undefined. We believed it was zero, but didn't know how to come to a definite conclusion. Date: 06/25/2003 at 12:19:04 From: Doctor Peterson Subject: Re: Infinity Hi, Joshua. Infinity itself is undefined! It is not a number, so you can't add anything to it. In a calculus class, you should be making a clear distinction between actual arithmetic and limits; we talk about infinity in the context of limits, where we are not really saying that we can add infinity and negative infinity, but rather that we can take the limit of the sum of two functions whose limits are infinity and negative infinity. In that setting, "infinity plus negative infinity" is indeterminate. This means that the limit of the sum depends on how the addends approach infinity. If one does so faster than the other, then it will govern the sum. We can't "determine" the limit of the sum without knowing the individual functions. See these pages for more: Indeterminate Forms http://mathforum.org/library/drmath/view/53353.html Why Are 1^infinity, infinity^0, and 0^0 Indeterminate Forms? http://mathforum.org/library/drmath/view/53660.html Note that these are called "indeterminate FORMS," not values. We don't actually treat infinity as a value when we do this; it is only the "form" of the limit that looks like "infinity minus infinity," and we have to change its form in order to evaluate it correctly. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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