The conversation between human and AI assistant.
If we can invent a number [math]i[/math] so that [math]i^2=-1[/math], why can't we have a number a so that [math]\sin a=2[/math]?
Are there any other functions like sine that have a limited domain of output values?
Yes, many functions have specific domains and ranges. For example, the natural logarithm only outputs positive values and the tangent function has vertical asymptotes at certain values. Understanding the domain and range of a function is crucial for understanding its behavior and using it in calculations.