Yes, two different ways of writing the same number.
Neither 1 or 0.99... exist, no more than the letter a. They're just symbols.
We could have chosen the symbol z for the sound 'a' instead. Wouldn't change anything. If you look at different handwritings, you will see several different shapes for the same letter. Same story.
It's like a caveman when numbers did not exist. One day he saw a mammoth. And he called him "mammoth". The the next day he saw two mammoths and he wondered how he was gonna call that. He decided that he was going to call that 2 mammoths, and the sighting of the day before was going to be 1 mammoth to differentiate. Then the 10th day he was sick of inventing new symbols so he got a brainwave and decided to start reusing the same symbols in sequence to designate even more mammoths.
And no wtf 0.11111... is not 0.
0.11111... is greater than 0.1 so it's not even close.
0.0000{insert infinite number of zeroes}1 is 0. You can write it 0.0...01
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