a. In (R, d) where d(x,y) = |x – y| (Euclidean Metric space) show that: Q (The set of all rational numbers) is dense (Q = R). b. Vx, y € Rk, x = (x1,x2, … ,Xk), y = (y1,y2, …,Yk) ... Show that: (ах Ву) 3D ав(х-у), Va, B € R

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a. In (R, d) where d(x,y) = |x – y| (Euclidean Metric
space) show that:
Q (The set of all rational numbers) is dense (Q = R).
b. Vx, y € Rk, x = (x1,X2,… ,Xk), y = (y1,Y2, ·.., Yk)
Show that:
( αχ . βy) αβ (x.y) να, β ε R
Transcribed Image Text:a. In (R, d) where d(x,y) = |x – y| (Euclidean Metric space) show that: Q (The set of all rational numbers) is dense (Q = R). b. Vx, y € Rk, x = (x1,X2,… ,Xk), y = (y1,Y2, ·.., Yk) Show that: ( αχ . βy) αβ (x.y) να, β ε R
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