First of all, it is important to note that the concept of infinity can be quite tricky to understand and apply in mathematics. It is possible that your gut feeling is correct, and there may be a mistake in your solution. It is always a good idea to double check your work and make sure that your answer makes sense.
In the context of signals and systems, infinity usually refers to the concept of unboundedness. This means that a signal or system can grow or decrease without limit. It is important to consider the context in which infinity is being used in a problem.
For example, if you are dealing with a continuous-time signal, it is possible for the signal to approach infinity but never actually reach it. This is known as a limit and is commonly used in calculus. On the other hand, in a discrete-time system, a signal can actually reach infinity if the values keep increasing without bound.
Another important consideration is the behavior of the signal or system as time approaches infinity. In some cases, the signal may approach a finite value as time goes on, even if it initially appears to be going to infinity. This is known as convergence and is an important concept in the study of signals and systems.
In conclusion, while it is possible for signals and systems to exhibit behaviors that approach infinity, it is important to carefully consider the context in which infinity is being used and to double check your work to ensure that your solution is accurate. As a scientist, it is important to approach problems with a critical and analytical mindset to avoid making mistakes and to fully understand the concepts at hand.
