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Is 0.999... a smaller number than 1?
No, 0.999... is not a smaller number than 1. They are exactly the same number, just represented differently. This is commonly misperceived because it looks like it should be ever so slightly smaller than 1, but mathematically it can be proven that they are equal.
No, 0.999... is not a smaller number than 1.

Here's the reasoning:

1. We can compare 0.999... to 1 by looking at their decimal representations.
2. When we write out the decimal representation of 0.999..., it goes on forever: 0.999... = 0.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999,9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999900990999999099999999999099999999999999999999999999909909999000900099999900999990009999999009909999999999999999999999999990999999990099990999999999999999999999999999999999999999099999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999599999999999999999999999999999th99999999999999999999999999999t9999999999999999999999999999999999999999t999999999999ttt999999999999999999999999999999999999t9999999999999999999999999999999999999999999999999999999999999999999999999999999999999ttt99999999tttt9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999t999999999ttt999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999ttthttt99999999999999999999999999999999999999999999999999999999999999999999