course mth 151 I am slowly comprehending this stuff. I will learn it! íF–ÎÒ¤ÆòÆ«¸ä”•þwÌ¡šnª|C{z‡¥†×÷ûassignment #005 005. `Query 5 College Algebra 01-30-2007
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22:32:23 Query 2.5.12 n({9, 12, 15, ..., 36})
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RESPONSE --> 10- there are 10 elements in this set and it isn't aleph-null since we know where it stops, right? confidence assessment: 3
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22:32:37 ** There are 10 numbers in the set: 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 **
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RESPONSE --> I understand self critique assessment: 3
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22:33:43 Query 2.5.18 n({x | x is an even integer }
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RESPONSE --> I put ( c ) because there would be only one element. confidence assessment: 3
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22:35:08 ** {x | x is an even integer } indicates the set of ALL possible values of the variable x which are even integers. Anything that satisfies the description is in the set. This is therefore the set of even integers, which is infinite. Since this set can be put into 1-1 correspondence with the counting numbers its cardinality is aleph-null. **
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RESPONSE --> I was not thinking about all the possible values. Though it would be aleph-null because it is infinite. self critique assessment: 3
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22:36:45 Query 2.5.18 how many diff corresp between {stallone, bogart, diCaprio} and {dawson, rocky, blaine}?
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RESPONSE --> ther can only be three since they are equivalent but not infinite. confidence assessment: 3
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22:38:10 ** Listing them in order, according to the order of listing in the set. We have: [ {S,D},{B,R},{Dic.,BL}] , [{S,bl},{B,D},{Dic.,R}], [{S,R},{B,Bl},{dic.,D}] [ {S,D},{B,DL},{Dic.,R}], [{S,bl},{B,R},{Dic.,D}], [{S,R},{B,D},{dic.,B1}] for a total of six. Reasoning it out, there are three choices for the character paired with Stallone, which leaves two for the character to pair with Bogart, leaving only one choice for the character to pair with diCaprio. **
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RESPONSE --> so you would use the 123, 231, 321, 132, 213, 312 rule huh? self critique assessment: 3
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22:41:55 2.5.36 1-1 corresp between counting #'s and {-17, -22, -27, ...}
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RESPONSE --> [ -17<->1, -22<->2, -27<->3, ...5-n<->n, ...] confidence assessment: 1
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22:43:21 **You have to describe the 1-1 correspondence, including the rule for the nth number. A complete description might be 1 <-> -17, 2 <-> -22, 3 <-> -27, ..., n <-> -12 + 5 * n. You have to give a rule for the description. n <-> -12 - 5 * n is the rule. Note that we jump by -5 each time, hence the -5n. To get -17 when n=1, we need to start with -12. THE REASONING PROCESS TO GET THE FORMULA: The numbers in the first set decrease by 5 each time so you need -5n. The n=1 number must be -17. -5 * 1 = -5. You need to subtract 12 from -5 to get -17. So the formula is -5 n - 12. **
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RESPONSE --> I almost had a beat on it. I was trying to do the same thing but did not use the proper language. self critique assessment: 3
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22:44:07 2.5.42 show two vert lines, diff lengths have same # of points
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RESPONSE --> They have a point at the bottom of the line and the top of the line don't they? confidence assessment: 2
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22:46:09 ** This is a pretty tough question. One way of describing the correspondence (you will probably need to do the construction to understand): Sketch a straight line from the top of the blue line at the right to the top of the blue line at the left, extending this line until it meets the dotted line. Call this meeting point P. Then for any point on the shorter blue line we can draw a straight line from P to that point and extend it to a point of the longer blue line, and in our 1-1 correspondence we match the point on the shorter line with the point on the longer. From any point on the longer blue line we can draw a straight line to P; the point on the longer line will be associated with the point we meet on the shorter. We match these two points. If the two points on the long line are different, the straight lines will be different so the points on the shorter line will be different. Thus each point on the longer line is matched with just one point of the shorter line. We can in fact do this for any point of either line. So any point of either line can be matched with any point of the other, and if the points are different on one line they are different on the other. We therefore have defined a one-to-one correspondence. **
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RESPONSE --> So no matter what, if the two lines stop then you can always draw a line to P. self critique assessment: 2
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