Continuity of a Function Over a Closed Interval

[matheyyy]

Hi all,

My maths professor stated the following in one of our recent lectures, claiming that the function y=x over the interval [-1,1] IS NOT CONTINUOUS.



I am perplexed since the definition of continuity over a closed interval is as follows;


Does y=x over the interval [-1,1] not meet these criteria? I understand why the function tan(x) over the interval [-π/4, π/4] is not continuous since the limits at each 'end' of the interval don't exist as the function is unboundedly approaching infinity, but I can't seem to understand why the previously mentioned function is not.


Thanks and appreciate the help in advance!

 

[blamocur]

I am perplexed too. You will need to ask your professor why he thinks the function is not continuous. Looks like a type to me.

 

[blamocur]

I understand why the function tan(x) over the interval [-π/4, π/4] is not continuous

I don't. Could they mean [imath][-\pi/2, \pi/2][/imath]?

 

[Steven G]

All lines, except vertical lines, are continuous over and open or closed interval