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The reason I subconsciously did it was that natural numbers have an inherent structure to them. You can describe all natural numbers using only the objects 0 an
by drx 16y ago
The reason I subconsciously did it was that natural numbers have an inherent structure to them. You can describe all natural numbers using only the objects 0 and succ, where succ = (+ 1).
An interesting fact is that this is sufficient to express + and :
a + 0 = a
a + (succ b) = succ (a + b)
a 1 = a
a * (succ b) = a + a * b
One way to look at structures (like, say, natural numbers) is too look at what really defines them, as in, what is absolutely necessary and sufficient to define them? In this case, 0 and succ is.
Note that I'm not saying you're wrong, everyone is entitled to their own definition of beauty. Isn't that the beauty of it?
- est 16y ago> I subconsciously did it was that natural numbers have an inherent structure to them. I understand and concur you :) But I don't think Euler's identity is meant to serve this purpose. Maybe some other formula. It's hard to un-like something once you already liked it very much. First impression matters. How about e^(i*pi)-1==0 instead?