document.write( "Question 495075: Can you give me lots of examples, and the definition of a real number, rational number, irrational number, and integers. Please and thank you. \n" ); document.write( "
Algebra.Com's Answer #335942 by Edwin McCravy(20060) $\"\"$ $\"About$
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document.write( "REALS:\r\n" );
document.write( "All numbers that are not imaginary are REAL numbers.\r\n" );
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document.write( "INTEGERS:\r\n" );
document.write( "The INTEGERS consist of the counting numbers 1,2,3,4,...\r\n" );
document.write( "and zero 0 and also the negatives of the counting numbers,\r\n" );
document.write( "-1,-2,-3,-4,... but no numbers in between them.\r\n" );
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document.write( "RATIONALS;\r\n" );
document.write( "The rational numbers are all the numbers you can make by \r\n" );
document.write( "making a fraction with an integer for the numerator and an\r\n" );
document.write( "integer for the denominator.  But you cannot use 0 for a\r\n" );
document.write( "denominator.\r\n" );
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document.write( "Here are some rational numbers , \r\n" );
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document.write( "All integers are also rational numbers because, for example,\r\n" );
document.write( "the integer 7 can be written as  and both the numerator\r\n" );
document.write( "and the denominator are integers.\r\n" );
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document.write( "Negative fractions such as  are also rational numbers \r\n" );
document.write( "because for example  can be written as either  or \r\n" );
document.write( "as .   \r\n" );
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document.write( "Decimals that end, such as 7.85 are rational because for example, 7.85\r\n" );
document.write( "can be written as  which reduces to \r\n" );
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document.write( "Decimals that don't end but which repeat a block of digits forever are\r\n" );
document.write( "rational numbers, for example  = 0.6666666... \r\n" );
document.write( "3.76363636363... can be written as , (divide that out and see).\r\n" );
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document.write( "IRRATIONAL\r\n" );
document.write( "These are simply numbers that are not rational.  They can only\r\n" );
document.write( "be approximated by irrational numbers or written with special symbols\r\n" );
document.write( "such as √ ∛ ∜ or p.\r\n" );
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document.write( "When they are approximated with decimals, the decimals never repeat\r\n" );
document.write( "a block of digits.  Many people think p is the\r\n" );
document.write( "same as the rational numbet .  However, if you divide that out\r\n" );
document.write( "you get\r\n" );
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document.write( " = 3.142857142857142857... \r\n" );
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document.write( "and it keeps repeating 142857 over and over forever.  However p is only close to that,\r\n" );
document.write( "not exactly that, for the decimals of p are:\r\n" );
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document.write( "p ≈ 3.141592653589793238 and\r\n" );
document.write( "those decimal digits go on forever with no pattern whatsoever.\r\n" );
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document.write( "(We use a wavy equal sign ≈ to indicate \"approximately equal to\").\r\n" );
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document.write( "When irrational numbers are approximated by decimals, they sometimes have\r\n" );
document.write( "a pattern to the digits, such as this one:\r\n" );
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document.write( "7.2233222333222233332222233333...\r\n" );
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document.write( "but it is irrational but it doesn't repeat the same block of digits,\r\n" );
document.write( "but increases the length of the block of 2's and 3's each time.\r\n" );
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document.write( "Edwin
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