wtf wrote:Addition is a binary operation. The only way to define addition of infinitely many summands is to define it as the limit of the sequence of partial sums.

Yes, addition is a binary operation. It is a function that takes two values and outputs a single value. We know that. Do you have anything else to say? Because you are repeating yourself.

You seem to think that an expression such as "2 + 2 + 2" represents an operation of addition that takes three values and outputs a single value. If that's what the expression stands for then it contradicts the definition of the word "addition". As you say, addition takes two inputs; but this expression, you also claim, represents a function that takes three. How can it then be addition? It cannot be -- unless you change the definition of the word "addition" that is. Fortunately for us, that's not what the expression stands for. It stands for a chained series of additions where the result of the first addition (which is "2 + 2") is taken as the input of the second addition. This means that you DO NOT have to redefine the concept of addition. You DO NOT have to extend it so that it can take three (rather than merely two) values as its input.