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8.(a) Give a direct proof that when w, x are real numbers such that w|sx|, we have \w + x] 2 (b) s |x| Recall that a subset TCS of a countable set S will also be countable. Use proof by contradiction to show that a superset W2V of an uncountable set V must also be uncountable.

8.(a) Give a direct proof that when w, x are real numbers such that w|sx|, we have \w + x] 2 (b) s |x| Recall that a subset TCS of a countable set S will also be countable. Use proof by contradiction to show that a superset W2V of an uncountable set V must also be uncountable.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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8.(a) Give a direct proof that when w, x are real numbers such that |w|s|x], we have \w + x| 2 (b) s |x| Recall that a subset TCS of a countable set S will also be countable. Use proof by contradiction to show that a superset W2V of an uncountable set V must also be uncountable.
Transcribed Image Text:8.(a) Give a direct proof that when w, x are real numbers such that |w|s|x], we have \w + x| 2 (b) s |x| Recall that a subset TCS of a countable set S will also be countable. Use proof by contradiction to show that a superset W2V of an uncountable set V must also be uncountable.
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