Give an indirect proof for d(x_n,y_n)→d(x,y)

Riya Andrews

Riya Andrews

Answered question


Give an indirect proof for
d ( x n , y n ) d ( x , y )

Answer & Explanation

Colin Dougherty

Colin Dougherty

Beginner2022-09-07Added 8 answers

An "indirect proof" usually starts with "Suppose not." So to go about this, suppose d ( x n , y n ) does not tend to d ( x , y ) as x n x, y n y. Then there is an ϵ 0 > 0 such that there exists no N such that for all n N,
| d ( x n , y n ) d ( x , y ) | ϵ 0
Now use the triangle inequality as in the direct proof to get a contradiction.

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