does 0.9999999.......... equal 1

**Correction**I incorrectly characterized part of Con's argument.I had subtracted 9 from 10x, not 9 from x; my bad.Subtracting 9 from x would give you 10x, Con is right...but*Algebraically ...999.0 = -1 Makes Sense*I mean, I'm not a math guy, but it seems to me that if in fact algebraically one could prove that 0.999... = 1 then it would follow that its polar opposite, ...999.0 i.e. the repeating decimal consisting of infinitely many 9s in the opposite direction, would be -1.Heck, I'll even take it further.-0.999... = -1and-...999.0 = 1This does not change the fact that algebraically 1 and 0.999... are indistinguishable from each other even if it seemingly counter-intuitively implies that an infinite positive value like ...999.0 is negative.In this case, both things are true, which actually makes sense.*Responding to Con*Con claims:"I said [0.333...] is not a correct value of 1/3 because it resorts to infinity which means there will never be an answer that satisfies the expression of 1/3."My response:Con focus here!Why does dividing 1 by 3 and dividing 0.999... by 3 give the same answer?If you're going to use your logic from above, you therefore consider 0.999... "not a correct value" yet using this not correct value when dividing by 3 is EXACTLY THE SAME as dividing 1, a value I assume you think is correct, by 3.Questions for Con:1. Con do you think 1 is an incorrect value?When you divide it by 3, you get, as you call it, an incorrect value, so the number 1 is necessarily made of 3 of those incorrect values.2. Why are 3 incorrect values equal to a correct value, but 1 incorrect value is not?3. I would also like Con to explain how it is that we divide ANY NUMBER by 3 without multiplying it by 0.333...Can Con give an example of dividing by 3 where the same answer cannot be reached by multiplying by 0.333...?Well everyone, 1/3 = 0.333... even if Con tells you it doesn't.Con reasserts:"You said that 1-0.999... equals 0.000...There is still a 1 at the end of it. But it is being pushed back by infinitely many nines."My response:Con, focus again!I correctly stated that the only time you see a 1 in the difference between 1 and 0.999... is when there's AN END to the 9s, which, right here you just admitted there is no end to by referring to INFINITELY many nines.Con childishly repeats:"There is still a 1 at the end of it."My response:Why would there be a 1 at the end of something which you just admitted HAS NO END?No end to the 9s-->no end to the answer-->no 1 at the end of the answer.Con appeals to ignorance:"Just because you will never find it, does not mean that it isn't there. That is why it is infinitesimally small."My response:I do hate this fallacy, and this example is most certainly an argument from ignorance given that it's appealing to not being able to find something as a reason to believe in its existence, but since we're talking about INFINITELY repeating 9s, I actually will never find the end, because INFINITY MEANS HAS NO END.The end is not infinitesimally small; it's infinitesimally not there.*Wrap Up*Well I corrected myself in that Con was actually correct in saying that 10x = x - 9 with his ...999.0 example, and I realized that (...999.0 = -1) actually makes perfect sense given that algebraically 0.999... is proven to equal 1 and having the repeating 9s go the other way could be achieved by adding a negative sign to it.I have not touched Con's ...999.999... example because it's really just total infinity and is not a rational number, so its behavior in algebra seems largely irrelevant to the question of whether or not 0.999... = 1.Con has not shown why 1 divided by 3 and 0.999... divided by 3 are the same.Con also has not been able to show an END to the answer of the subtraction problem 1 - 0.999...Con?