Is a ruler an example of metric spaces? I was reading metric spaces and tried to think about some real life example of metric spaces. I think it will be a metric space.  Am I correct? 
 A: That will depend a bit on what you mean by "ruler". You have to use a mathematic definition of such object.
But let's assume that you by a ruler means a line segment accompanied with a scale, that is a linear assignment of "length markings" ranging from 0 up to some maximal value. And then define the distance between two point as the absolute difference in these markings. 
Then yes it's a metric space, it's isomorph to the real line segment from 0 to the maximal value which in turn is a metric space.
A: I would argue that for most humans, imagining "spaces" that are not metric spaces is more difficult! Our daily lives are littered with metric spaces. Sometimes you think about how many blocks you need to walk, sometimes you talk about how many hours you need to drive. In American Football you only really care about the single dimension of yardage, despite having a two dimensional football field. A great deal of the definitions in topology have direct inspiration from metric spaces and are just attempts at generalizing this idea.
