Can You Draw a Right-Continuous Function with No Left Limit?

[wayneckm]

Hello all,


I am just curious about whether it is possible to DRAW a right-continuous function (without left limit). Apparently the answer is negative to me since whenever we use a pen and draw an arbitrarily short line, it must be continuous there.


Wayne

 

[HallsofIvy]

I'm not sure what you mean by this.

The function y= f(x) where f(x)= 0 for x< 0, f(x)= 1 for x\ge 0 is right continuous at x= 0 and is easy to graph. Of course, there will be an ambiguity as to what happens at x= 0 unless you use the standard convention: draw a "filled circle" at the point (0, 1) to indicate that that end of the ray is included in the graph and an "open circle" at the point (0, 0) to indicate that that end of the ray is not included in the graph.

 

[Petr Mugver]

http://en.wikipedia.org/wiki/Continuous_function

 

[steve9409]

Hello all,


I am just curious about whether it is possible to DRAW a right-continuous function (without left limit). Apparently the answer is negative to me since whenever we use a pen and draw an arbitrarily short line, it must be continuous there.


Wayne

not sure what you mean by draw. Maybe f(x) = sin(1/x) for x<0 and f(x) =1 for x>=0