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All elements in the following union are distinct, therefore the union is a set. | All elements in the following union are distinct, therefore the union is a set. | ||
| − | <math> S_1 \cup S_2 = \{ \frac{1}{2 | + | <math> S_1 \cup S_2 = \{ \frac{1}{2}, 1, 1.4, 2, 17 \} </math> |
[[Image:Lecture_3.PNG| 360x360px]] (<math class="inline"> S_1 \cup S_2</math> represented by colored region.) | [[Image:Lecture_3.PNG| 360x360px]] (<math class="inline"> S_1 \cup S_2</math> represented by colored region.) | ||
:<span style="color:green">WOW! That's a VERY nicely written answer. Great work. You only missed one little (somewhat tricky) detail. Can you guess what it is? MATH MAJORS: Can you help him? </span> -pm | :<span style="color:green">WOW! That's a VERY nicely written answer. Great work. You only missed one little (somewhat tricky) detail. Can you guess what it is? MATH MAJORS: Can you help him? </span> -pm | ||
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| + | :Okay, | ||
| + | :<math class="inline">\frac{1}{9} = 0.\bar{1}</math> | ||
| + | |||
| + | :<math class="inline">\frac{1}{9} * 9 = 1</math> | ||
| + | |||
| + | :<math class="inline">\frac{1}{9} * 9 = 0.\bar{9}</math> | ||
| + | |||
| + | :<math>\therefore 0.\bar{9} = 1</math> | ||
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=== Answer 2 === | === Answer 2 === | ||
Revision as of 07:31, 12 January 2013
Contents
Practice Problemon set operations
Consider the following sets:
$ \begin{align} S_1 &= \left\{ \frac{1}{2}, 1, 1.4, 2 \right\}, \\ S_2 & = \left\{ 0.\bar{9}, 1.40, \frac{42}{21}, 17\right\}. \\ \end{align} $
Write $ S_1 \cup S_2 $ explicitely. Is $ S_1 \cup S_2 $ a set?
You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too!
Answer 1
All elements in the following union are distinct, therefore the union is a set.
$ S_1 \cup S_2 = \{ \frac{1}{2}, 1, 1.4, 2, 17 \} $
($ S_1 \cup S_2 $ represented by colored region.)
- WOW! That's a VERY nicely written answer. Great work. You only missed one little (somewhat tricky) detail. Can you guess what it is? MATH MAJORS: Can you help him? -pm
- Okay,
- $ \frac{1}{9} = 0.\bar{1} $
- $ \frac{1}{9} * 9 = 1 $
- $ \frac{1}{9} * 9 = 0.\bar{9} $
- $ \therefore 0.\bar{9} = 1 $
Answer 2
The union of S1 and S2 is all the elements in the Venn diagram: in S1, S2, and in both S1 and S2.
Answer 3
Write it here.
