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]?
What other examples of mathematical concepts exist that don't have physical analogues like [math]i[/math]?
There are many examples, such as infinite sets or irrational numbers like [math]\pi[/math] or the square root of 2. These concepts don't have direct physical interpretations, but they are still useful in mathematics and help us understand the world around us better.