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RE: Ego Studies #1 - Introduction to complex numbers
There are so many question. D: But I will start with why you want to compare imaginary numbers to integers. Integers are discrete. Imaginary numbers are not discrete. D:
I was waiting for your input :P
My answer is actually quite simple:
I wanted to work with examples people can relate to. For me it was important to explain the basic idea behind imaginary numbers to people without any previous knowledge about them. I'm fully aware there is much more to say and my approach is quite simplistic (But honestly, my professor didn't care to make that distinction as well - so why should I? :P ) - but in my opinion it's important to get the basic ideas first and then dive into details and how these affect the ideas.
Using DNA samples to explain a cat to someone who has never seen a cat is quite pointless - you get my idea?
Seeing the whole number numbers as two directions and comparing them with the complex numbers as a to dimensional object is a good idea.
As set the whole number are not really special, because the whole number and natural numbers are both countable sets.
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I am trying to point out the following:
So imaginary numbers is the set given by all the real numbers times i. So it is a continuous spectrum. Then it makes sense to compare them to the real numbers.
Similarly, when dealing with the integers in this setting you might want to compare them to the set given by multiplying all the integers times i.
That is a defense not a answer to my question. I explained my question in more detail in response to a comment of quekery.