now i understand both intersection and union but not with an infinity. how do i figure this out

(-infinity,4)n(0,infinity)

To understand how to find the intersection of two intervals that involve infinity, such as (-∞, 4) ∩ (0, ∞), we can break it down as follows:

1. Start with the first interval, (-∞, 4). This represents all real numbers that are less than 4 (excluding 4 itself) and extends towards negative infinity.

2. Next, consider the second interval, (0, ∞). This represents all real numbers that are greater than 0 and extends towards positive infinity.

3. Now, we need to find the common elements between these two intervals. To do this, we look for the overlapping region between the two intervals.

Since the first interval, (-∞, 4), only goes up to 4 (excluding 4 itself), and the second interval, (0, ∞), starts from 0 (excluding 0 itself), there is no overlap between the two intervals. This means that there are no common elements between these two intervals, and thus the intersection of (-∞, 4) and (0, ∞) is an empty set or ∅.

In summary, the intersection of (-∞, 4) and (0, ∞) is an empty set because there are no common elements between the two intervals.