> 0, 1, +, , ^, which are sufficient to express all of elementary natural arithmetics (unless I'm mistaken)
Well, personally I don't favor zeros in equation. What's the point of 1+0=1 ?
Leaving 0 on the right side looks so unbalanced.
Well, personally I don't favor zeros in equation. What's the point of 1+0=1 ?
Leaving 0 on the right side looks so unbalanced.
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?
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?