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08:50:53 ** There are 10 numbers in the set: 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 **
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RESPONSE --> n= 10 because there are 10 numbers from 9 to 36 that are multiples of 3.
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08:51:51 Query 2.5.18 n({x | x is an even integer }
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RESPONSE --> the cardinal number of even integers is aleph-null. they would be {-2,2,4,6,...}
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08:53:29 ** 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 --> There would be 9 different possibilities (subsets) which is set A or 3 times set B, also 3
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08:54:17 2.5.36 1-1 corresp between counting #'s and {-17, -22, -27, ...}
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RESPONSE --> yes, a one to one corr. can be set up between counting #'s and {-17,-22,-27,...} because the cardinality of both is aleph-null
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08:56:31 ** 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 --> you just have to make a one to one correspondence between the 2 vertical lines to get the same # of points, the length of the line shouldn't matter, just the distance between any two points.
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}͖bրҎ assignment #006 j{̜e܌xeų Liberal Arts Mathematics I 01-26-2006
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08:59:20 Query 1.1.4 first 3 children male; conclusion next male. Inductive or deductive?
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RESPONSE --> inductive reasoning becuase it's based on previous examples
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09:00:23 Query 1.1.8 all men mortal, Socrates a man, therefore Socrates mortal.
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RESPONSE --> Socrates is a mortal is deductive reasoning because it's based on accepted terms and applied to them. i call them ""facts"" in the problem because they are assumed to be true.
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09:01:20 Query 1.1.20 1 / 3, 3 / 5, 5/7, ... Probable next element.
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RESPONSE --> the next probable element would be 7/9 becuase each number was 1/3, 3/5, 5/7...
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09:02:57 Query 1.1.23 1, 8, 27, 64, ... Probable next element.
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RESPONSE --> the first three elements seemed to be 1 cubed, then 2 cubed, then 3 cubed and 4 cubed, so i would say the next element is 5 cubed or 125
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09:04:05 Query 1.1.36 11 * 11 = 121, 111 * 111 = 12321 1111 * 1111 = 1234321; next equation, verify.
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RESPONSE --> the next equation would be 11111x11111=123454321 because that follows the pattern. this is indeed a true statement also
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09:04:41 Do you think this sequence would continue in this manner forever? Why or why not?
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RESPONSE --> i expect this sequence would continue forever as long as we keep using only 1's to mulitply by
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09:05:54 Query 1.1.46 1 + 2 + 3 + ... + 2000 by Gauss' method
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RESPONSE --> Gauss's method would say there are 1000 pairs of 2001 which gives us 2,001,000
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09:07:46 Query 1.1.57 142857 * 1, 2, 3, 4, 5, 6. What happens with 7? Give your solution to the problem as stated in the text.
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RESPONSE --> it gives us a bunch of 9's. by multiplying the first 6 by 142857 we could see it coming
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09:08:20 What does this problem show you about the nature of inductive reasoning?
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RESPONSE --> it shows inductive reasoning is not always right.
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