🚀 go-pugleaf

Hi, Russell. I hope you don't mind me butting in here.
Your question is a very good one. In fact I would encourage you to continue asking such questions since they are at the heart of what maths is all about, i.e. a language of symbols which do not necessarily have to have any inherent meaning. You see in maths, at least in my opinion, it is the relationship between the symbols and the patterns that they create that contain most of the meaning and not the symbols themselves. 
To attempt to answer your question

 RL>  I just finished reading your letter and decided that I would ask you
 RL> the question that my teacher didn't care to explain. What is an
 RL> 'imaginary number'? How can you get the square root of a negative
 RL> number? 

Essentially   i or the square root of minus one has no inherent meaning. Instead it represents an unknown which is implied by certain mathematical rlationships. For example, to solve for the roots of certain types of quadratic equations we assume the existance of  i or i-squared. We can then say certain things about the behaviour of such equations or functions, such as that they exhibit oscillation patterns, without necessarily being able to say anything about the imaginary ellement itself.
I'll pose you another tricky questiowhich is central to modern math.
What exactly does the zero symbol mean, and can the concept of complete absence have any inherent meaning in the real world? The answer is not a simple yes. In fact arguably the zero symbol has no inherent meaning. It simply helps mathematicians represent certain types of relationships they would not otherwise be able to represent.
Anyway, Russell think about what I have said. There is no reason why you have to agree with me... It is by disagreement that we learn.
Perhaps you can think of other examples of maths symbols that don't appear to have any inherent meaning.

P.S. I am no a teacher. In fact I am a student of economics at university in New Zealand, attempting to understand the world of maths just like you.

Anyway, bye for now,    Andrew


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