The sets I₀=[2,5] and I₁=[3,4] intersect over the interval [3,4], which is where both sets overlap on the real number line.
The question addresses the intersection of two sets, I₀ and I₁. The intersection of two sets includes all the elements that are common to both sets. In this case, both I₀=[2,5] and I₁=[3,4] are intervals on the real number line. The intersection would therefore be the set of all real numbers that are included in both intervals.
To find the intersection, we look for the overlapping range of the two intervals. Since I₀ starts at 2 and ends at 5, while I₁ starts at 3 and ends at 4, the common range between these two intervals is from 3 to 4. This means that any real number between 3 and 4, including 3 and 4 themselves, will be in the intersection of I₀ and I₁.
So, the intersection of the sets I₀=[2,5] and I₁=[3,4] is the interval [3,4]. That is the range where they both overlap.
The intersection of I₀ and I₁ is simply where the two sets overlap, which for intervals translates to the shared range. In this explanation in 150 words, we found that the intersection of the sets is the interval [3,4].