My Math Forum Proof That a Rational lies between two Irrationals

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May 23rd, 2017, 12:39 AM   #11
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Quote:
 Originally Posted by v8archie Just truncating the upper one might work.
How about rounding up the smaller number then truncating AFTER the first decimal position where they differ?

Your counter example would be done thus:

$0.2989989998...$ would be rounded to

$0.3000000000... \ \ \$ <-- rounded up value of smaller number
$0.3010010001... \ \ \$ <-- unchanged value of larger number

They now differ at the 4th decimal position so

$\frac{0.300 + 0.301}{2} = 0.3005$

and this is in between the original 2 numbers

 May 23rd, 2017, 03:48 AM #12 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,675 Thanks: 2655 Math Focus: Mainly analysis and algebra

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