CalcNotes0203-page1 - Something approaching ± ²(generally...

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(Section 2.3: Limits and Infinity I) 2.3.1 SECTION 2.3: LIMITS AND INFINITY I PART A: INFINITY The topic of infinity is a very rich one, and it has different interpretations. (See Footnote 1 and Wikipedia , for example.) We will not consider infinity to be a real number, although the real number system can be extended to include infinity. The symbol for infinity is ± . We write negative infinity as ±² . (See Footnote 2.) When something approaches ± along the real number line, it (generally) increases without bound. If you give me any real number, this thing will exceed that number. We will make this idea more precise in a later section.
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Unformatted text preview: Something approaching ± ² (generally) decreases without bound. PART B: NOTATION FOR NONEXISTENT LIMITS We say that a limit exists ± it exists as a single real number. If it is appropriate to write that a limit is ± or ± ² , then we will do so, even though the limit still technically does not exist. (However, we can say that the limit exists in the “extended reals”; See Footnote 1.) If a limit does not exist, and ± and ±² are inappropriate, then we will write “DNE.” That is, the limit does not even exist in the “extended reals.”...
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