JusttoLearn
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- 2023
without counterexamples, please
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Proof Help: How to prove that between two distinct rational numbers, there exists an irrational number (1 Viewer)
- Thread starter JusttoLearn
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a+(b-a)/r2 is between a and b,
and rational + irrational = irrational.
JusttoLearn
New Member
- Joined
- Mar 10, 2022
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- 3
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- HSC
- 2023
Can you present in like a hsc-standard, or be a bit more specific. How did you come up with "a+(b-a)/r2," what is 'r,' so I can know how its between a and b.
r is root. i wanted a + (b-a)/x where x is irrational, x>1, to make rational + irrational = irrational number between a and b. a + (b-a)/r2 = a+r2(b-a)/2 was the choice.
consider the equation as vectors for some intuition, WLOG assume b>a,
a + (b-a)/r2 is a vector between a and b since r2>1.
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