isolatedvertex asked: e is the base of the natural logarithm, and if you have never heard of it, explaining it to you would take more characters than I can put in this ask. This is my point exactly: people often say the real numbers are familiar and the complex numbers are some sort of black magic, but that's not true at all. A lot of complex numbers can be explained in very simple terms, which is more than you can say about a lot of real numbers.
Thank you,
I’ll reply to all 3 messages in one:
RE: the above (and all of these, actually)
If it’s too much to get into, could you provide source(s) that would be helpful?
I { droped math } at about Trig, so something that would explain things well but simply. I’m planning on getting back into it soon (calculus specifically), but until then I’d be interested in a mathematical nonfiction for introductory purposes.
RE:
“Edit: The definition of i as i*i+1=0 sort of eludes me. I’m not sure what the rule is, to use it in other equations. i*i is then -1? But then what is i?”
i is the number such that i*i = -1. :) Starting form the integers, every number is defined in terms of other numbers and operations. For example, 1/2 is the number such that (1/2)+(1/2) = 1.
Fair, but I know how else to use 1/2 — I can understand what half of 3 is or half of an apple is. I can’t understand what i is in any other terms.
RE:
It says “the real numbers are everything you’ve ever worked with”. That’s not really a definition at all (have you ever worked with e before learning about exponential functions?), and actually, constructing the real numbers is a quite convoluted process (see Wikipedia: Construction of the real numbers). On the other hand, like I said constructing (some of) the complex numbers is very easy, it involves only the basic operations of addition and multiplication, and the integers.
The main reason I looked into real numbers vs integers was the Continuum Hypothesis: “There is no set whose cardinality is strictly between that of the integers and that of the real numbers.”
I had no idea what they were, so maybe it’s not the best definition, but the examples helped me get a practical idea about them.
Again, if you could provide better references, that’d be great.
All that stems from this question, which maybe you could also add insight too since you’re a mathematician:
blog comments powered by Disqus36
Infinite Networks:
If there are infinity points in a network, and each point is directly connected to every other point, is the number of connections between them > infinity?
Is this even a useful question?from { Notes from Q&J: Questions }
