For any two rationals, a and b, such that a<b,
0 < b−a
0 < (√2/2)·(b−a)
a < a+(√2/2)·(b−a)
= a+√2·((b−a)/2)
┆√2/2 < 1┆
< a+(b−a)
= b
a+√2·((b−a)/2) is irrational and lies between two rationals.
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213 ∀a,b∈ℚ and a≠b, ∃c in (a,b) and c∉ℚ |
| by EngliSea on 2020-07-16 | |
| ᐥBetween any two distinct rationals there is an irrational.ᐥ For any two rationals, a and b, such that a<b, 0 < b−a 0 < (√2/2)·(b−a) a < a+(√2/2)·(b−a) = a+√2·((b−a)/2) ┆√2/2 < 1┆ < a+(b−a) = b a+√2·((b−a)/2) is irrational and lies between two rationals. |
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