– why is 0.999… equal to 1?

Question

I know the Arithmetic proof and everything but how to explain this practically to a kid who just started understanding the numbers?

In: 3202

Answer 1

One way to define what a number actually **is**, is to create something called a Dedekind Cut. In simple terms, I can “slice” the number line at a certain point and put all the points on the line to the left in one collection and all the point on the line to the right in another collection. Then, I can say that a number is “equal to” the collection running off to the left.

The set which defines 0.999… has precisely the same points in it as does the set that defines 1, so they are the same number.