I know the Arithmetic proof and everything but how to explain this practically to a kid who just started understanding the numbers?
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> how to explain this practically to a kid who just started understanding the numbers?
As a parent, it might be a smidge too early for this concept. (I’m basing it on “just started understanding the numbers”)
Another way to view it is that you cannot write down, in any way, any number that is between 0.999… and 1
The difference is just 0.000… and there’s never anything other than zeros
It’s just an artefact of notation
As a rule, between any two real numbers, there must be another real number. There is no number between .999… and 1, therefore they are the same, simply two ways of writing the same number. If the kid is the curious type, it might be pretty interesting to point out that numbers are conceptually separate from their representation. Most simply: ½=.5, but there’s also binary or hexadecimal, or even more exotic forms (like p-adic or continued fractions). The numbers themselves sorta “exist” out there in the aether as an abstract object that isn’t exactly tied to our notation.
Maybe more like explaining like you are 9, but I’d go with this:
Pick any number that you want. Is that number less than 1? Then it is easy to show that it is also less than 0.999……. The same is true if the number you choose is greater than 1. If both of those things are true then 1 and 0.999999…. have to be equal.
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