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Double sharp (talk | contribs) →Continuity: since we just mentioned tan, I guess we should note that it is (pretty clearly) not continuous at infinity either |
Reverted 1 edit by Double sharp (talk): Tan is conti (TW) |
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: <math>\tan\left(\frac{\pi}{2} + n\pi\right) = \infty\text{ for }n \in \mathbb{Z},</math>
then tan is continuous in <math>\mathbb{R}</math>. However, many [[elementary function (differential algebra)|elementary function]]s, such as [[trigonometric functions|trigonometric]] and [[Exponential function|exponential]] functions, are discontinuous at <math>\infty</math>. For example, sin
Thus 1/''x'' is continuous on <math>\widehat{\mathbb{R}}</math> but not on the [[affinely extended real number system]] <math>\overline{\mathbb{R}}</math>. Conversely, the function arctan can be extended continuously on <math>\overline{\mathbb{R}}</math>, but not on <math>\widehat{\mathbb{R}}</math>.
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