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Unformatted text preview: (Section 2.3: Limits and Infinity I) 2.3.29 FOOTNOTES 1. Infinity. Infinity is not a number in the usual real number system that we will study in calculus. The affinely extended real number system, denoted by or , , includes two points of infinity, one referred to as (or + ), and the other referred to as . (We are adjoining them to the real number system.) We obtain the twopoint compactification of the real numbers. We never refer to and as real numbers, though. Sometimes, and are treated as the same (we collapse them together and identify them with one another as ), and we then obtain the onepoint compactification of the real numbers, also known as the real projective line. Then, we can write 1 = , and we can say that the slope of a vertical line is . A point at infinity is sometimes added to the complex plane, and it typically corresponds to the north pole of a Riemann sphere that the complex plane can be thought of as wrapping...
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 Fall '10
 sturst
 Calculus, Limits

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