When you say 'i=0', what you mean is that that is the base case, and the sigma specifies a bunch of other cases.
i_1 =/= i_2.
As xg15 noted, it's perfectly fine to say (x=2) => (x + 3 = 5). The problem the first example really addresses is that in mathematics, the namespaces are loosely defined, but in programming they aren't. 'i' can mean several things at once, and it doesn't really matter because those things never really interact in the same context. In programming, you need to specify the name 'i' every time you want to reference it, so it's important that you have a stricter namespace rule.
i_1 =/= i_2.
As xg15 noted, it's perfectly fine to say (x=2) => (x + 3 = 5). The problem the first example really addresses is that in mathematics, the namespaces are loosely defined, but in programming they aren't. 'i' can mean several things at once, and it doesn't really matter because those things never really interact in the same context. In programming, you need to specify the name 'i' every time you want to reference it, so it's important that you have a stricter namespace rule.