Wholes (W):<\/em>\u00a0\u00a0{0,1,2,3,4…..}\u00a0 These include all the naturals, plus zero.<\/p>\n Integers (Z):<\/em>\u00a0\u00a0{….-3,-2,-1,0,1,2,3….}\u00a0 These include all the whole numbers, plus the negatives of them.<\/p>\n Rationals (Q):\u00a0 <\/em>You can’t list these numbers in order, since there is always another one between any two you name.\u00a0 However, you can define them as follows:\u00a0 a rational number consists of any integer divided by an integer\u00a0other than\u00a0zero.<\/p>\n In other\u00a0words,<\/p>\n rational=integer1\/integer2<\/p>\n where integer1 can be zero, but integer2 cannot be zero.\u00a0 Therefore, rationals include the following examples:<\/p>\n Hence, we see that any integer, since it can be written as itself over 1, is rational.<\/p>\n It turns out that rationals also include repeating decimals as well as terminating ones. You can verify the facts on your calculator:<\/p>\n 409\/99=4.1313131313…..<\/p>\n and of course<\/p>\n -12\/5=-2.4<\/p>\n Up to and including the rationals, each set contains the previous one.\u00a0 That is, the rationals contain the integers, the integers contain the wholes and\u00a0the wholes contain the naturals.\u00a0 However, the next set of numbers – called the I<\/em>rrationals<\/em> – is completely different from the rationals and separate from them.\u00a0 The irrationals contain non-repeating, non-terminating <\/em>decimals.\u00a0 These numbers are written symbolically:\u00a0 examples are \u221a(11), as well as our friend π.<\/p>\n The Real Numbers (R)<\/em> contain all the rationals, plus all the irrationals.\u00a0\u00a0There is yet another set:\u00a0 the\u00a0Imaginary Numbers<\/em>.\u00a0 We’ll save them for another post.<\/p>\n![\"\"](\"\/..\/rational.png\")
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