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let a and b be two sets such that there exists a function f from a onto b and a function g from b onto a show assuming
1 show assuming ac that any cartesian product of finite sets is either finite or uncountable cant be countably
1 in the partially ordered set n times n with the ordering j k le m n iff j le m and k le n consider the sequence n
1 prove without applying theorem 151 that the well-ordering principle implies ac caution is it clear that the
if x is uncountable and y is a countable subset of x show that x y has the same cardinality as x assuming that n has
1 prove that for any countably infinite set s there is a 1-1 function from n onto s hint let h be a function from n
1 to define the factorial function f n n by simple recursion how can c and h in corollary 133 be chosen for h to
1 for any two relations e and f on the same set x define a relation g e f by xgz iff for some y xey and
1 an amount of r25 000 is invested at an interest rate of 11 per annum compounded half-yearly fornnbspyears find the
a couple decides to save to buy a car in two years time they will invest a fixed sum into a two-year fixed deposit
hillstone sa manufactures and sells tyres to the passenger vehicle market in southern africa the quarterly sales in 1
the economic statistics bureau has recorded the number of company liquidations over 27 time periods as
the level of advertising expenditure in the financial services sector ie banks insurance investments to promote
the following table represents the quarterly value of healthcare claims in r millions against all medical health
the following table reports both the seasonal indexes for all national park visitors and the number of visitors to the
1 there are 23 people at a party explain what the probability is that any two of them share the same birthday 2 a
a share trader has a policy of selling a share if its share price drops more than one-third of its purchase price in
the department of marine resources reports the number of tonnes of pelagic fish caught off the west coast during each
the following table gives the gross domestic product gdp in r100 millions for a certain african country from 2001 to
the table mountain cable car company recorded the following data on the number of tourists in thousands who visited
the number ofnbspnew business registrationsnbspin the gauteng region was recorded by the department of trade and
the management of an office complex in central johannesburg wants to understand the pattern of energy consumption ie
the marketing manager of a company that manufactures and distributes farming equipment such as combine harvesters
the seasonal indexes and actual quarterly turnover in r millions for 2008 2009 and 2010 in the hotel industry in cape