course Mth 151 I checked over my assignments posted, and was alarmed when 2.4 popped up twice, and 2.5 didn't show at all. So just in case I forgot to post it, here's 2.5, and I apologize about the mixup. XŽï…¾Òžïzxå§k‚سïÄöï~assignment #005
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22:34:18 Query 2.5.12 n({9, 12, 15, ..., 36})
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RESPONSE --> The cardinal number of 9 to 36 equals 10 I got this by simply filling in the elipses with the missing numbers and received (9,12,15,18,21,24,27,30,33,36) By simply counting those, I received n(A)=10 confidence assessment: 3
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22:34:24 ** There are 10 numbers in the set: 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 **
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RESPONSE --> OK self critique assessment: 3
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22:36:44 Query 2.5.18 n({x | x is an even integer }
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RESPONSE --> The cardinal number is aleph-null, as in can be put into a 1-1 correspondence with counting numbers, and the set itself is infinite. confidence assessment: 2
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22:36:51 ** {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 --> OK self critique assessment: 3
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22:38:58 Query 2.5.18 how many diff corresp between {stallone, bogart, diCaprio} and {dawson, rocky, blaine}?
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RESPONSE --> I can only assume that this problem is supposed to be number 24 in my book, in which I had {Foxx, Myers, Madonna} <-> {Ray, Austin, Eva} Using all possibilities except for the one that repeated theirselves, I found 6 different correlations between these sets. confidence assessment: 1
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22:40:01 ** 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 --> This is one of numerous times I have been confronted with problems that aren't in the book or even the correct number, but I got the general gist of the problem itself, and I'm pleased I managed to get it correct despite the incorrect labeling. self critique assessment: 2
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22:42:45 2.5.36 1-1 corresp between counting #'s and {-17, -22, -27, ...}
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RESPONSE --> The numbers in the set {-17, -22, -27...} decrease by 5, so you would use -5n as part of the formula. The correspondence can be 1 <-> -17, 2<-> -22, 3<-> -27.....n <-> -5n confidence assessment: 2
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22:43:34 **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 --> Ok I understand, it was tricky at first, but everything involving one to one correspondences are confusing to me at first. I do think I went deep into the problem enough to get the general gist, or at least a good grasp on it. self critique assessment: 2
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22:45:12 2.5.42 show two vert lines, diff lengths have same # of points
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RESPONSE --> I was actually very stumped by this question, and I skipped it altogether as I did not understand. confidence assessment: 0
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22:45:59 ** 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 --> I am still throughly confused on the correspondence of these lines, as I've never dealt with lines and drawings before when it comes to finding a correspondence. self critique assessment: 1
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