Suppose a newly-born pair of rabbits‚ one male‚ one female‚ are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male‚ one female) every month from the second month on. The puzzle that Fibonacci posed was how many pairs will there be in one year? When attempting to solve this problem‚ a pattern is detected:
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Cardinal numbers: Definition‚ Examples Cardinal numbers We know that‚ the relation in sets defined by A~ B is an equivalence relation. Hence by fundamental theorem on equivalence relation‚ all sets are partitioned into disjoint classes of equivalent sets. Thus for any set A‚ equivalence class of A‚ [A] = { B | B ~ A } Result: - (1) [A] = [B] or [A] ∩ [B] = ∅ ‚ that is for any two sets‚ either they have same equivalence classes or totally disjoint equivalence classes.
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Mathematical Puzzles These puzzles (most of them old classics) from various sources can be used with pupils who finish classwork early. Most of the questions were chosen with enthusiastic‚ bright early teenagers in mind. Some of the puzzles are also appropriate for class work - an initial worked example on the board will help a lot. There are a few trick questions. Some questions can be quickly answered if you chance upon the right approach‚ but the ’long’ solution isn’t too arduous. Several of
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SHOULD AN ASPIRING STUDENT GO FOR A COURSE WHICH IS IN DEMAND OR FOR A COURSE WHICH HE/SHE LIKES? Introduction: The student should go for the course that they want because it’s their Enjoyment that is important rather than pressure of society of what is demand/not. But still it’s their choice‚ so think wisely & don’t force them in a thing that They may regret in end How to choose once career? Do an analysis with open mind. The student alone knows that one particular course they may not like
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After viewing the film ‘Born Rich’‚ which profiled young adults who were born into the upper 1-4% of the wealthiest families in the country‚ I was kind of surprised to see that the majority of them did not like for it to be known that they came from money and still wanted to work for their own money. Also I found it classy that the parents insisted that even though they had inherited all this money‚ they were still responsible for doing something with their lives‚ and could not depend primarily on
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demonstrated in Numbers. In a similar way as in Exodus‚ Gods’ provision and work in Israelites was constantly present‚ despite their continued disobedience. The establishment of the tabernacle was still emphasized in Numbers‚ the laws and regulations that they had to obey and live by. Ultimately‚ their rebellion only worsened their situation‚ God taught them a lesson‚ in which He was in control and their sinful choices brought great suffering and caused the wrath of God upon them. In Numbers‚ the establishment
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Boys and Girls Alone Is reality TV for kids? Where is the line between fair reality and cruel displays of innocent people? And who is the actual victims‚ us or the participants? Boys and Girls Alone is a reality show broadcasted on Channel 4 in February 2009‚ and it has raised a lot of ethical questions and moral issues from concerned experts. With TV broadcasters that are free to edit their footage‚ and with viewers who watch reality-TV just to catch a break and turn off their brains for a few
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REAL NUMBERS Q.1 Determine the prime factorization of the number 556920. (1 Mark) (Ans) 23 x 32 x 5 x 7 x 13 x 17 Explanation : Using the Prime factorization‚ we have 556920 = 2 x 2 x 2 x 3 x 3 x 5 x 7 x 13 x 17 = 23 x 32 x 5 x 7 x 13 x 17 Q.2 Use Euclid’s division algorithm to find the HCF of 210 and 55. (1 Mark) (Ans) 5 Explanation: 5 ‚ Given integers are 210 and 55 such that 210 > 55. Applying Euclid’s division leema to 210 and 55‚ we get 210 = 55 x 3 + 45 ………
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The Number Devil The Number Devil - A Mathematical Adventure‚ by Hans Magnus Enzensberger‚ begins with a young boy named Robert who suffers from reoccurring nightmares. Whether he’s getting slurped up by a giant fish‚ sliding down an endless slide into a black hole‚ or falling into a raging river‚ his incredibly detailed dreams always seem to have a negative effect on him. Robert’s nightmares either frighten him‚ make him angry‚ or disappoint him. His one wish is to never dream again; however‚
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Alone From childhood’s hour I have not been As others were; I have not seen As others saw; I could not bring My passions from a common spring. From the same source I have not taken My sorrow; I could not awaken My heart to joy at the same tone; And all I loved‚ I loved alone. Then- in my childhood‚ in the dawn Of a most stormy life- was drawn From every depth of good and ill The mystery which binds me still: From the torrent‚ or the fountain‚ From the red cliff of the mountain‚ From
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