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Last sentence should be:

Since it has been shown there exists a number that is greater than 0.(9) but less than 1, 0.(9) != 1.


Wow, this comment system is shit.

Last sentence should be:

Since it has been shown there exists a number that is less than 1, but greater than 0.(9), 0.(9) != 1.


Doing this as more of a thought experiment if you had .9 and 9 repeating infinitely it would approach and equal 1. In actual practice you can never actually reach infinity because well it is the nature of infinity.

I think that is sort of the bump that confuses a lot of people. The people who say it does not equal 1 seem to be in the mind frame that infinity will just create an infinitely small difference that gets smaller and smaller and small for infinity, but still leaving a difference.

The side that says they equal each other seem to look at it from more of a hypothetical where infinity is reached, even if you can't really ever get to infinity.

The thing is that these sort of hypothetical assumptions are done all the time in various fields and they usually seem to be accepted without much question. The exception to this seems to be with infinitely repeating digits.

I mean, if you can accept absolutely no friction in a thought experiment, why not accept infinity being reached? Or you could just take the easy route and use significant digits.

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