Question

Prove that any infinite subset of the discrete metric space is bounded.

Answer 1

@Alchemista

Answer 2

please help

Answer 3

@eliassaab

Answer 4

@amistre64

Answer 5

@SolomonZelman

Answer 6

Look at the definition of the distance function. You will see that a ball of radius greater than \(1\) is enough to bound any points in a discrete metric space.

Answer 7

d(x,y)=0 if x=y
d(x,y)=1if x is not equal to y
.@Alchemista

Answer 8

As @Alchemista said, take any point x in the space and take a ball B of center x and radius 2, then the whole space is contained in B