The twenty-five members of the mathematics club must send a delegation to a meeting for student groups at their school. The delegation can include as many members of the club as desired, but at least one member must attend. How many different delegations are possible? (Type a whole number.)

Step 1 ：The problem is asking for the number of ways to form a delegation from a group of 25 members. This is a combination problem, where the order of selection does not matter.

Step 2 ：However, since the delegation can include as many members as desired but at least one member must attend, we need to consider all possible combinations from 1 to 25.

Step 3 ：This is equivalent to finding the power set of a set with 25 elements, minus the empty set (since at least one member must attend).

Step 4 ：The power set of a set with n elements has \(2^n\) elements, so the power set of a set with 25 elements has \(2^{25}\) elements.

Step 5 ：Subtracting the empty set gives us \(2^{25} - 1\) possible delegations.

Step 6 ：Final Answer: The number of different delegations possible is \(\boxed{33554431}\).