Exercise · ZW-DENSITY-OF-THE-RATIONALS-005 · ★☆☆ Basic
Which number lies between \(0.999\) and \(1\)?
Choose one option.
Show answer
- B. \(0.9995\)
Explanation
\(0.9995\) satisfies \(0.999<0.9995<1\). The others are below \(0.999\) or equal to \(1\).
Review the concept: Density of the rationals
Property of the rationals \(\mathbb Q\) inside the reals: between any two distinct reals \(a<b\) there is always a rational \(q\).
\[a
More practice problems: density of the rationals
- ZW-DENSITY-OF-THE-RATIONALS-001 Between any two distinct reals there is always:
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- ZW-DENSITY-OF-THE-RATIONALS-003 Which rational lies between √2 and √3?
- ZW-DENSITY-OF-THE-RATIONALS-004 Is there a positive rational smaller than all the others?
- ZW-DENSITY-OF-THE-RATIONALS-006 The rational midpoint of tfrac27 and tfrac37 is:
- ZW-DENSITY-OF-THE-RATIONALS-007 In the density proof with a=0.3 and b=0.4, take n=11 with tfrac1n<b-a and m=lfloor narfloor+1. Whic…
- ZW-DENSITY-OF-THE-RATIONALS-008 Which of these numbers between 1 and 2 is irrational?
- ZW-DENSITY-OF-THE-RATIONALS-009 Between two reals a<b there are:
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