half bounded and half open intervals

[viperrr]

Hi, my question is whether or not half bounded and half open intervals are the same. As in, would this : [-12, +infinity) qualify as both bounded and half open?

I understand that a bounded interval has two endpoints that may coincide, and that an open interval excludes its endpoints. Half bounded endpoints have one endpoint and extends indefinitely on the other side. I'm just not familiar with the term half open.


Thanks in advance!

 

[daon2]

Hi, my question is whether or not half bounded and half open intervals are the same. As in, would this : [-12, +infinity) qualify as both bounded and half open?

I understand that a bounded interval has two endpoints that may coincide, and that an open interval excludes its endpoints. Half bounded endpoints have one endpoint and extends indefinitely on the other side. I'm just not familiar with the term half open.


Thanks in advance!

It is half-open but not bounded. A bounded interval must be bounded from below and bounded from above.

 

[HallsofIvy]

Hi, my question is whether or not half bounded and half open intervals are the same. As in, would this : [-12, +infinity) qualify as both bounded and half open?

No, this is an "unbounded" closed interval. It is neither "bounded" nor "half open". The ")" at infinity does not indicate "open" or "closed". Whether an interval extending to infinity is open or closed depends entirely upon what happens at the other end. (-infinity, +infinity) is both open and closed. We never use "[" or "]" at infinity because "infinity" is not a number and cannot be included in an interval.

I understand that a bounded interval has two endpoints that may coincide, and that an open interval excludes its endpoints. Half bounded endpoints have one endpoint and extends indefinitely on the other side. I'm just not familiar with the term half open.

The intervals [0, 1) and (0, 1] are "half open".

Thanks in advance!