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In simple arithmetic the basic operations of addition, subtraction, multiplication and division are all binary.

That means you need two numbers, one on each side of the operation, for an expression to be valid.

For example in one plus three, the word plus is a binary operation acting on the two numbers one and three.

Similarly in four times three, the word times, acting as a proxy for 'multiplied by' is again a binary operation acting on the two numbers four and three.

You get the point.

So what about one plus one? Can this ever be read as one added to itself?

In the expression 1 + 1 it sure looks like there are two numbers. The 1 before the plus sign and the 1 after the plus sign.

OK what about 2 x 3? Mathematicians and teachers initially teach this as repeated addition.

Some say two times three is two added to itself three times.

Yet the word 'itself' is a third person singular reflexive pronoun.

Surely you cannot add a number to itself!!!

Add one apple to itself.

Multiplciation requires a multiplicand (number of obects) and a multiplier (the active factor).

So 2 x 2 cannot be two multiplied by itself

Multiply two apples by themselves!

So my question is does the use of the reflexive pronoun 'itself' in binary arithmetic operations defy logic?

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closed as not constructive by FumbleFingers, James McLeod, Mitch, Carlo_R., tchrist Feb 25 '13 at 13:33

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Don't take things so literally. himself, herself, ...what if you don't know the sex...itself. The rest of your question might be relevant to mathematics.SE. – Mitch Feb 25 '13 at 1:27
What @Mitch says. If you try and puzzle that out you'll be at it 'til the cows come home. – Jim Feb 25 '13 at 2:04
Why can't I add a number to itself? Sure, I can't do that with apples, but apples aren't numbers to begin with. – jwodder Feb 25 '13 at 5:04

"Itself" in these expressions simply means "the same number" or "a number of equal value". It's just a lexical shortcut that everyone understands, not an existential problem. Every "1" is equal to every other "1"; they're fungible, like clones. It's a standard idiom in math class, so, as Mitch says, don't be so literal when interpreting the expression. It has a recognized meaning in context: "Add 1 to itself" = "Add 1 and 1".

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