document.write( "Question 772528: Is there a least fraction on a real number line? Explain \n" ); document.write( "

Algebra.Com's Answer #470946 by solver91311(24713) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "No. Suppose you create a fraction 1 over a denominator that is 1 followed by a hundred zeros and then assert that this is the smallest possible fraction. I can disprove your assertion simply by adding a one hundred and first zero to your denominator number. And if I then had the temerity to assert that NOW we have the smallest possible fraction, all you would have to do is add one more zero. And this game could go on forever without anyone actually creating the \"least\" fraction.\r
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\n" ); document.write( "\n" ); document.write( "Works the same way with very big numbers. If you say you have the biggest number, I can just add 1, or add

for that matter, and I have just made a number bigger than your \"biggest\" number.\r
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\n" ); document.write( "\n" ); document.write( "It also works with finding numbers between two numbers. For any two numbers on the real number line, no matter how close they are, there are an infinite number of numbers between those two numbers. For example, we talked earlier about to very tiny fractions:

and

. But as tiny as those are, and as close as they are, there are an infinity of other numbers between those two. \r
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\n" ); document.write( "\n" ); document.write( "John
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\n" ); document.write( "Egw to Beta kai to Sigma
\n" ); document.write( "My calculator said it, I believe it, that settles it
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