Here’s another way to look at it. If 0.99999… does *not* equal 1, there must be some number greater than 0.99999… and less than 1, because the real numbers are defined as infinitely divisible – there are infinite numbers between any two numbers you can name.
What is that number between 0.99999… and 1? How can you express that number in decimal if every place in 0.99999… has a 9, and there’s no digit greater than 1?
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