Is Number 1 the First Number?

Is Number 1 the First Number?

I like to think that number 1 was the first number invented. After all, it's very basic to have just one of something. Most people avoid 0 and start counting with 1, so in that respect it can be considered the first number, or as mathematicians like to call them, the positive integers {1,2,3,...}.

What else can we say about the number 1? Well, notice that if you multiply any number by 1 the number remains unchanged. That is, n*1=n for any number n. So mathematicians say that 1 is the "identity element" of the multiply operation. Identity just means it doesn't change anything under the operation.

The multiply operation, like many in mathematics, is called a binary operation for the simple reason that it works with two objects.

So, if 1 is the identity for the multiply (*) operation is it also the identity for the addition (+) operation? No, not at all, because n+1 is not equal to n.

While we're on the subject of the addition operation we can also say that 1 is the most fundamental number in the sense that any positive integer can be made from 1 by just adding it to itself enough times n=1+1+........+1 where n is any positive integer.

Of course, under the multiply operation this will get you nowhere, since 1*1*1...*1=1 and that's what you would expect from the identity element of an operation.

Wow. Look at all the mathematical jargon we've used.. "positive integers", "binary operation", "identity element". Pretty impressive!

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Content written and posted by Ken Abbott