top | item 34441677 (no title) johnnny | 3 years ago k * √2 is an integer, and k is an integer, by construction of K and the initial assumption that K is not empty.Therefore their difference k * √2 - k = k * (√2 - 1) is an integer. discuss order hn newest janm31415|3 years ago correct, I missed that. johnnny|3 years ago As fro your further edit: assuming √2 is rational, then the set of ~~rational~~ integers {q: q√2 ∈ ℤ} does not admit a minimum, indeed it contains arbitrarily small numbers, so we can't pick k the smallest member of that set.
janm31415|3 years ago correct, I missed that. johnnny|3 years ago As fro your further edit: assuming √2 is rational, then the set of ~~rational~~ integers {q: q√2 ∈ ℤ} does not admit a minimum, indeed it contains arbitrarily small numbers, so we can't pick k the smallest member of that set.
johnnny|3 years ago As fro your further edit: assuming √2 is rational, then the set of ~~rational~~ integers {q: q√2 ∈ ℤ} does not admit a minimum, indeed it contains arbitrarily small numbers, so we can't pick k the smallest member of that set.
janm31415|3 years ago
johnnny|3 years ago