Difference between a standard and metric?

[math6]

hi friends can someone help me and explain for me what is the difference between a standard and metric?

 

[radou]

The standard metric usually refers to the euclidean metric, i.e. the "standard euclidean" metric.

 

[HallsofIvy]

hi friends can someone help me and explain for me what is the difference between a standard and metric?

I do not recognize the term "a standard". I wonder if you didn't see the phrase "standard metric" that randou refers to. The "standard metric" on $R^n$ is
$$d((x_1, x_2, ..., x_n),(y_1, y_2, ..., y_n))= \sqrt{(x_1-y_1)^2+ (x_2-y_2)^2+ \cdot\cdot\cdot+ (x_n-y_n)^2}$$

 

[Fredrik]

Perhaps it should have been "difference between a standard and non-standard metric", in which case you're both right, but I still win.

 

[disregardthat]

In general a metric need only satisfy the three conditions
*) d(x,y)=0 --> x=y
**) d(x,y)=d(y,x)
***) d(x,y)+d(y,z) <= d(x,z)
and there can be many such metrics. The standard euclidean metric is only one example.

 

[HallsofIvy]

I kind of wish math6 would get back to us and explain what he meant!